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OUTLINES OF LOGIC 



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•J. H. GILMORE, A.M., 



PROFESSOR OF LOGIC, RHETORIC AND ENGLISH IN THE 
UNIVERSITY OF ROCHESTER. 



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ROCHESTER, N. Y., 

PRINTED FOR THE AUTHOR BY THE EVENING EXPRESS PRINTING CO. 

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THE LIBRARY! 

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Copyright, 
J. H. GILMORE. 

1876. 



OUTLINES OF LOGIC. 

1. What is the relation between Psychology, Logic 
and Rhetoric ? 

Psychology (ftvxr/ and \6y05) discusses the powers and 
processes of the human mind ; while Logic treats of the 
products of the human mind. 

Practically, however, Psychology is restricted to those 
mental processes by which the mind accumulates and retains 
the materials for thought ; while not merely the products of 
the human mind, but the processes by which the materials for 
thought are elaborated and organized, are remanded to Logic. 

Note. In strictness, conceiving, judging and reasoning fall, 
fairly, within the scope of Psychology ; while concepts, judg- 
ments and reasonings belong to the domain of Logic. It is 
better, however, to have some one science entrusted with 
matters so closety related as the processes and products of the 
same mental faculties. 

It will be seen, at once, that Logic and Psychology are 
intimately related. The student ought, really, to have some 
knowledge of Psychology before entering upon his Logical 
studies — that is : he should study the mind and its processes 
before attempting to examine, scientifically, the products of 
the mind ; he should know how the mind collects, and retains, 
the materials for thought before lie attempts to learn how the 
mind uses the materials for thought. In some colleges, a 
term in Psychology wisely precedes the study of Logic. We 
must content ourselves, however, with the incidental illustra- 



4 OUTLINES OF LOGIC. 

tion of such Psychological problems as thrust themselves 
upon us from time to time. 

While Logic is thus grounded in Psychology, it has its 
outcome in Rhetoric— whose province it is to give clear, 
forcible and elegant expression to Logically - developed 
thought, and Elocution — whose province it is orally to 
deliver, in an appropriate and effective manner, thought 
adequately expressed. The following diagram illustrates the 
relation of these studies : 



ELOCUTION. 



RHETORIC. 



LOGIC. 



PSYCHOLOGY. 



2. What do we mean when we speak of the Faculties 
of the Human Mind ? 

By a faculty of the mind, we mean the mind's capacity 
for working in a given direction. Thus, when we speak of 
;t the moral faculty," we mean, simply, the mind's capacity 
to decide on questions of right and wrong. The wisest 
philosophers regard man's spiritual nature as an entity ; and 
maintain that, however varied its manifestations, it is really 
one and indivisible. When we classify the operations of the 
mind, and* enumerate its faculties, let it be distinctlv under- 

i 



OUTLINES OF LOGIC. 



stood that, so far as the mind itself is concerned, our division 
is purely factitious. We have merely stretched certain line- 
athwart the object-glass through which we inspect the mental 
processes. The mind has not, like the body, a hand for this 
service, a foot for that, and a stomach for the other. It is, in 
the strictest sense, a unit. "The mental faculties" is but a 
convenient phrase for the unit of consciousness as it appears 
now in this, and again in the other, sphere of intellectual 
activity. 

3. Classify the faculties of the Conscious Subject, and 
state with which of these faculties Logic has to do. 

The following classification of the mental faculties — sub- 
stantially that of Sir William Hamilton — is sufficient for 
our purpose : 



r 



CONSCIOUS 
SUBJECT. 



r 



A. Cognitive j I. Intuitive 
Faculties. ^ Faculties. 



B. Emotive 
Faculties. 



II. Discursive 
Faculties. 



Preservative — Per- 
ception, external 
or internal. 

Re - presentative — 
Memory, Imagi- 
nation, etc. 



1. Con- 
ception. 

2. Judg- 
ment. 

3. Reas- 
oning. 



C. Con ati ve 
Faculties. 

L 

Note. Atwater (Logic, p. 27, note) would add Constructive, 
or Plastic. Imagination to the Discursive Faculties. And 
with reason ; since Constructive Imagination must conform 
strictly to Logical rules. For this very reason, however, it 
docs not require recognition here — falling, naturally, under 
the head of Conception. 



6 OUTLINES OF LOGIC. 

3: a. Define "subject" and "subjective." 
Define "object" and "objective" 
Define " cognitive," "emotive" and "conative." 

"Subject" is restricted, in scientific usage, to the mind 
that thinks — the ego. "Object" is applied to that about 
which the mind thinks — the non-ego. If the mind thinks 
about itself, it would be denominated the " subject-object." 
"Subjective" naturally means: relating to the mind that 
thinks : " objective," relating to that about which the mind 
thinks. See Thomson, Laws of Thought, p. 35 note. 

The " cognitive" faculties (cognoscere, to know) are those 
which have to do with the acquisition of knowledge. The 
" emotive" faculties (emovere, to excite) have to do with the 
feelings. The "conative" faculties (conari, to endeavor) 
have to do with the will. "The intellect, the sensibilities 
and the will " is the nomenclature formerly employed to mark 
these distinctions ; but is open to objection, as suggesting 
different centres of mental activity, which do not really exist. 

3 : b. Explain what is meant by the intuitive as 
distinguished from the discursive faculties. 

The " intuitive " faculties (in and tueri) are those which, 
by immediate, face-to-face contact, either with external 
objects or internal states, furnish the mind with the materials 
for thought. These faculties give us mental presentations of 
individual objects, and groups of objects — not of classes. 
Thus, by intuition, the mind grasps the idea of a book, or 
books ; but not the. generic notion, book. General notions 
are elaborated from the individual presentations of the 
intuitive faculties by the "discursive," or elaborative, faculties, 
whose office it is to work up the material thus presented. 
The "intuitive" faculties bring together the materials for 
the structure of thought: the "discursive" faculties arrange 
and combine those materials. Losnc has to do with the 



OUTLINES OF LOGIC. 7 

"discursive" faculties alone. It has nothing to do with 
collecting the materials for thought, or testing their value — 
indeed, respecting their value pure Logic is utterly indiffer- 
ent : but is concerned simply with the task of correctly 
classifying them, comparing them and unfolding the 
inferences which may legitimately be deduced from such 
sification and comparison. 



3 : c. What do you understand by the " presentative" 
faculties ; the " re-presentative " faculties ? 

It may be said, in further explanation of our classification 
of the mental faculties, that the " preservative" faculties — 
including perception external and internal — are those which 
take cognizance of objects, or states of consciousness, that are 
actually present to the mind ; the ; * re-presentative" faculties, 
those which reproduce to the mind absent objects, or states of 
consciousness that it has formerly grasped. Under this last 
head, are included Memory and Imagination. 



3 : d. What are the different functions of Memory ? 

Memory has two functions. (1) To retain — often beneath 
the consciousness of the thinking subject — an object, or event, 
once presented to the mind. (2) To recall and identify an 
object or event once presented to the mind — and this, either 
through conscious elfort (recollection, reminiscence) or, invol- 
untarily, through the association of ideas (reiflemb ranee) . 
With reference to its first function — retention — memory has 
sometimes been called, quiescent; with reference to its 
lid function, 'Mice. This would give us the following 
clarification : 

j (Quiescent — simply retentive. 
Memory , . J Recollection — with conscious elfort. 
I ( Remembrance — without " 

By others, the word •■ memory" has been used with reference 
to the retentive activity ; the word w * recollection'' with refer- 
to the recalling and identifying activity of the mind. 



O OUTLINES OF LOGIC. 

3 : e. What do you understand by Imagination ; 
and what distinction is to be made between 
"simple" and "constructive" Imagination? 

Imagination is the image-making faculty. Says Descartes : 
" To imagine is nothing more than to contemplate the figure, 
or image, of a corporeal being." We ma}', however, imagine 
a sound, a smell, a taste, as well as a sight, by exciting the 
sensibility of the auditory, olfactory, or gustatory, rather than 
the optic, nerves — though the pictorial representation made to 
the ear, nose and mouth is not so vivid as that made to the 
eye. The materials employed by the imagination must be 
furnished by the presentative faculties, Hence, there can be 
no imagination apart from the retentive function of memory ; 
though there ma}' be imagination apart from the identifying 
function of memory. This is less likely to be the case in 
"simple" imagination — where the mind paints a picture of 
an object just as it was seen — than in " constructive," or 
" plastic" imagination, where the mind puts its materials 
together in new and unseen combinations. 

3 : /. In what relation do Memory and Imagination 
stand to each other ? 

It is generally conceded that, though imagination can act 
without the cooperation of memory in its identifying functions, 
memory cannot recall and identify without the activity of the 
imagination. Every thought must have its symbol. 

4. Define Logic, in the modern acceptation of the term. 

Logic (from AoyoS^ which denotes the senno interims as 
well as extemus) is " the science which treats of the neces- 
sary, or formal, laws of thought" — that is : of the principles 
in accordance with which all thinking that is worthy of the 
name must be conducted. 

4: a. What are we to understand by the word 
"thought," as used in Logic? 

Thomson, p. 19, defines "thought''' as "that active 
function of the mind, by which impressions received, either 



OUTLINES OF LOGIC. 9 

from within or without, are described, classified and com- 
pared." Hamilton (Logic, p. 15) says: •• The essential 
characteristic of thought is the comprehension of a thing 
under a general notion or attribute." Cf. Mansel, 
Prolegomena Logica, p. \Y2. 

When we think, we simply affirm, or deny, that an object 
possesses a certain attribute or belongs to a certain class. 
Three things are essential to thought: 1, an object; 2, an 
attribute or a class of objects; 3, affirmation or negation. 
e. g. The bird is flying ; John is not a soldier. 

Note, carefully, the restricted sense in which the word 
tk thought" is used. There may be great, and varied, mental 
activity ; yet no " thought," in the proper sense of that word. 
Thought, is the exercise of the " discursive faculties." Apart 
from the exercise of these IC faculties," there may be percep- 
tion, memory, simple imagination ; but there is no thought. 
See the author's Art of Expression, pp. 9, 10. 

4 : b. What do you understand by Law ? 

Law is " the constant and regular order according to which 
an energy, or agent, operates." Fleming, Vocabulary of 
Philosophy, p. 285. Any just conception of " law," involves, 
back of the law, an energy or agent. Laws do not enact, 
promulgate and enforce them-selves. The " law of gravita- 
tion," for instance, is simply the enunciation of the uniform 
method according to which a mysterious force acts. The 
wi laws of thought are simply the enunciation of the uniform 
methods in accordance with which the human mind acts in all 
correct thinking." See Jevons, Logic, p. 1. 

4 : c. What do you understand by a science as dis- 
tinguished from an art; and what reason is 
there for regarding Logic as a science rather 
than an art P 

••A science is a body of principles and deductions to 



10 OUTLINES OF LOGIC. 

explain some object-matter : an art is a body of precepts 
* * for the completion of some work. A science teaches 
us to know ; an art, to do" Thomson, p. 26. There has been 
much discussion whether Logic should be considered as a 
science only ; or an art only ; or as, in turn, both. See 
Jevons, p. 7. The tendency was, formerly, to regard it as an 
art ; but thus viewed, it should embrace instructions on all 
points which could facilitate reasoning on any subject (see 
Thomson, § 6), and would necessarily assume vast proportions. 
Logic is now regarded as a science in which those principles 
that underlie the process of reasoning, whatever its sphere, 
are explained and exemplified till the student understands 
them and can apply them, modified as the occasion demands, 
for himself. 

4 : d. What is meant by the " form," as ^distinguished 
from the " matter," of thought ? 

By "matter," we mean, in general, the material out of 

which an object is formed; by " form," the outline or shape 

which gives it its peculiar character. Thus, in a statue, the 

marble is the " matter" which might be changed to bronze, or 

wood, or putty ; yet, if the outline remains the same, it is 

* \ 
still a statue. 

The distinction here taken is different from the ordinary 
distinction between "matter and mind" or "matter and 
spirit." Thus, Thomson sa} x s : "Space may be regarded as 
* matter,' and geometrical figures as the ' form' impressed on 
it. The voice is the ' matter ' of speech; and articulation, 
the k form.'" (See Thomson, § 11, Jevons, p. 4 sq.) 

The "matter" of thought is that about which we think. 
The " form" of thought is what the mind impresses and, from 
its constitution, must impress on that about which it thinks. 
Thus, whatever the matter of thought may be, the mind im- 
presses on it the form of concepts, judgments, reasonings. 
In the Fordham Logic, for instance, we are told that the 



OITUNKS OF LOOtO. 1 1 

subject and the predicate constitute the matter of a propo- 
sition ; the copula, its form. The subject and predicate may 
be indefinitely changed : but, so long as there is a subject and 
a predicate united by a copula, we still have a proposition. 

Logic has to do exclusively with the form — not at all 
with the matter — of thought. "When we call Logic the 
science of the formal laws of thought, we mean that the 
science is only concerned with that which is essential to, and 
distinctive of, the thinking process." Thomson, p. 39. 
Cf. Fleming, p. 201, and Hamilton, p. 53. 

4: e. "What do we mean when we speak of the 
" necessary laws " of thought ? 

That there are certain laws in accordance with which the 
mind must think, if it think at all, no matter what the object 
of its thought may be. In order to be necessary, these laws 
must be : 

a. Determined b} T the nature of the thinking subject. 

b. Original and not acquired. 

c. Universal. 

See Hamilton, pp. 17-18, Thomson, § 9. 

5. How does the true object which Logic contemplates 
differ from that which is sometimes assigned to it ? 

See Thomson, § 45 and p. 82. Also, Bowen, Logic, p. 40. 

Logic has no trick, or device, to teach, which can make the 
dull student more than a match for him who is, by nature, 
keen and bright. In this popular misapprehension of its 
claims, it suffers from the extravagant pretensions of its early 
votaries. The true object which Logic contemplates is, 
simply, to analyze the processes of thought that we have been 
carrying on from childhood and explain the principles on 
which they have been conducted — showing how they have 
succeeded, and why they have failed. The simplest sentence 



12 OUTLINES OF LOGIC. 

that we utter is " a Logical judgment," and contains " a 
Logical concept." When we study Grammar, we really study 
Logic — or might study it, if we would only dig down through 
the sentences that we analyze to the underlying thought. See 
the author's Art of Expression, p. 6. 

Cf. M. Jourdain in Molk're's Bourgeois Gentilhomme: "Par 
ma foi, il y a plus de quarante ans que je dis de la prose sans 
que j'en susse rien." 

6. What is the distinction between Pure and Applied 
Logic ; and what is the natural order of their genesis ? 

" Pure Logic " treats of Logical principles considered in 
themselves, without regard to their practical application. 
"Applied Logic" treats of Logical principles as practical!}' 
employed in the discovery and vindication of truth. Without 
serious violence to language, " Pure Logic" might be called 
the science; "Applied Logic," the art of reasoning. 

The order of their genesis is : First, reasoning ; then, 
reasoning regularly conducted with a view to a practical end ; 
then, the science of reasoning — pure and simple. Or : first, 
Logical processes ; then, Logical precepts ; then, Logical 
principles. This is the natural order of development in any 
science. See Thomson, S£ 1-5. In the order of genesis, 
therefore, "Applied Logic" precedes "Pure Logic." 

7. What advantages may reasonably be expected from 
the study of Logic ? 

The advantage of Logical studies has been stoutly denied 
on account of the extravagant pretensions of the devotees of 
this science. < 

See Locke, as quoted in Whately's Logic, § 3 ; Macaulay, 
Essays, vol. 2, pp. 372, 395 sq. 

Their eulogies have, however, frequently been misinter- 
preted. Thus when Duns Scotus styles Logic : "Ars artium 



OUTLINES OF LOGIC. .13 

et scientia scientiarum, qua aperta, omnes aperiuntur, e£, qua 
clausa, omnes aliae dauduntur^ he does not mean that Logic 
is the best and highest of all the sciences, but the servant and 
minister of all — a fact which is attested by the further fact 
that " The very name of Logic occurs as part of nearly all the 
names recently adopted for the sciences, which are often 
vulgarly called the • ologies,' but are really the ; logics' — the 
' o ' being only a connecting vowel or part of the previous 
word, * * * Each science is thus confessed to be a 
special logic." Jevons, p. 6. 

That Logic has its uses — altogether apart from the satis- 
faction that is afforded by the investigation and analysis of 
our noblest mental processes — cannot, however, be success- 
fully controverted. These advantages are : 

1 . The mental discipline afforded by mastering its difficulties. 

2. The habits of accurate statement acquired by familiarity 
with a science whose terminology is so exact. 

3. The repression of tendencies to hasty and incorrect 
thinking, by the careful analysis of correct processes of 
thought. In this way — indirectly, but none the less surety — 
Logic teaches us to reason, b}^ showing us how men have 
reasoned. 

4. The ability acquired to detect and, b} r a system of con- 
cise and accurate nomenclature, expose fallacious reasoning 
in ourselves and others. The trained logician knows just 
where to look for the weak point in an argument, and just how 
to expose it when detected. See Hamilton, p. 35. 

5. The training imparted to the inferential, or suggestive, 
faculties. See Thomson, p. 79, who says: 

" The suggestive power may be educated as certainly as, 
though more gradually than, the critical. The discoveiw 
which we call a flash of genius, a happy thought, really 
depends as much upon previous acquirements, as the power 
of stating a case or applying a rule does. These bright 
suggestions never occur to the ignorant ; the}' have the facts 
before them, but their imaginations arc not trained to leap to 
the proper inference from them. All discipline of the suggest- 



14 OUTLINES OF LOGIC. 

ive must proceed from the critical power ; it is by a long, 
careful, patient analysis of the reasonings by which others 
have attained their results, that we learn to think more 
correctly ourselves." 

For illustrations of what Thomson here intends, see his 
Laws of Thought, p. 259 sq. Cf. Hamilton, p. 32. 

On the entire subject, see Thomson, gg 36, 37, 45 ; Whately, 
pp. xviii-xxii ; Everett, Science of Thought, pp. 3-4. 

8. Enumerate the sources from which Logic derives 
its materials. 

The sources from which Logic derives its materials are : 

1. Intuitions of the phenomena of the external world. 

2. Intuitions of the phenomena of the conscious subject. 

3. Intuitions of the structural functions of the conscious subject. 

8 : a. What questions have been raised respecting 
the validity of these sources of knowledge ? 

Two questions 'have been raised with reference to these 
alleged sources of knowledge — questions which it does not fall 
within the province of Logic to discuss and settle ; but which 
we ought, certainly, to note in passing. 

The first question is : Do the senses report to us truly con 
cerning the outward ivorld? On this point the popular view is 
that there is an external world which is precisely what the 
senses represent it to be. Certain philosophers, who are 
known as Idealists, affirm, however, that we have no certainty 
that the external world is what it seems to us to be — nay, 
some of them go so far as to affirm that we have no knowledge 
that an external world exists. All that we can know, they 
affirm, is certain sensible affections of the thinking subject. 
Aiv^thing beyond that is mere matter of inference, which may 
or may not be valid. Other philosophers, called Realists, 
insist that we know, through the senses, that there is an 
external world, and that the senses report to us correctly 
concerning the primary qualities of matter at least ; though 
they concede that, taken as a whole, our conception of the 



OUTLINES OF LOGIC. If) 

external world is the resultant of two determining causes — 
objective existence presented to the mind and the mind's 
peculiar activity in dealing with this objective existence. See 
Thomsoui^ 10; Masson, Recent British Philosophy^ p. 59 sq. ; 
and Everett, Science of Thought , pp. 13-22. This question 
must, of course, ho remanded to Psychology and Metaphysics 
— Logic being a formal science, and altogether indifferent as 
to the reality, or unreality, of the material with which it 
works. It may be said, however, that the presumption is in 
flavor of the credibility of the senses ; and that the burden of 
proof rests upon those who question the validity of this source 
of knowledge. 

The second question is : Has the mind structural functions 
which limit and condition it i)i dealing with the materials of 
thought f — does it, as Bacon allirins, t; like an uneven mirror, 
blend its own nature w r ith things as they are, distort and 
discolor them ?" or does the mind simpty reflect and register 
presentations, just as they are, without subjective modifica- 
tion? The first view is that of the Transcendental! sts, i. e., 
those who believe that there is something in the mind which 
transcends experience ; the second, that of the Emjnricists, 
who believe that all our knowledge is but transformed 
experience. 

The views of our modern Empiricists are adequately stated 
and ably combated in the Thceetetns of Plato. Triibner ed., 
vol. 1, p. 251. u For the man who knows anything seems to 
me to apprehend through the senses what he know r s ; and, 
indeed, as it now appears, knowledge is nothing else than 
sense-perception . ' ' 

For our present purpose, we assume the correctness of the 
first view. See Thomson, g£ 32, 33, and Masson, p. 34 sq., 
p. 48 sq. 

8 : b. What do you understand by the structural 
functions of the mind ; necessary truths ; 
super -sensuous truths ; a priori truths ? 

When we speak of the l * structural functions of the human 
mind," we mean that the mind is not a plane mirror, reflecting 
and registering, without modification, impressions received 
from some determining agency ; but is so constituted that it 
must work in certain directions and develop certain ideas 



16 OUTLINES OF LOGIC. 

which mere sense-perception could never confer upon it. 
Such ideas are those of time, space, cause and effect, the 
axioms of mathematics — and, in general, those ideas the 
contrary of which is unthinkable. These truths are called 
necessary truths, because, so soon as the mind begins to think 
it cannot fail to apprehend them ; because it accepts and holds 
them instinctively, without regard to any process of demon- 
stration by which they are established. Necessary truths 
require to be comprehended ; but they do not require to be 
proved. That two straight lines cannot enclose a space would 
not, probably, strike us as a self-evident truth if it were stated 
in Choctaw. These truths are also called supersensuous 
truths ; because no amount of mere generalization from the 
data afforded by the senses can account for that imperative 
necessity with which the mind invests them, and which is 
their most distinguishing characteristic. See Mansel, pp. 92 
(especially note) and 97. They are also called a priori truths ; 
because, to borrow the language of Hamilton, " they are 
potentially in the mind, anterior to the act of experience by 
which they are first elicited in consciousness ;" but it is not- 
claimed by Hamilton, or any modern philosopher, that they 
actually exist in the mind prior to experience. 

9. What are the three general divisions of Pure Logic ? 

(1) Conception, w T hich treats of the method of forming 
general notions. 

(2) Judgment, which treats of the comparison of notions to 
test their agreement or disagreement with each other. 

(3) Reasoning, which treats of the method of deducing 
one judgment from another judgment, or other judgments. 

9 : a. Is the order in which they are discussed in 
Logical text-books the natural order P 

In pursuing the study of Logic, two methods are open to us, 
the analytic and the synthetic. Adopting the analytic 



OUTLINES OF LOOIO. 17 

method, we should break up the finished argument of au 
orator: 1, into reasonings ; 2, into judgments; ;), into con- 
cepts or general notions. This would, of necessity, be our 

method it' we were attempting to create a science of Logic; 
and then we should, naturally, discuss the general divisions of 
OUT subject in the following order: 1, Reasoning; 2, Judg- 
ment : 3, Conception. The process of analysis has, however, 
been gone through with again and again, and all its results 
are before ns. We can, therefore, if we prefer, adopt, as 
more convenient for purposes of instruction, the synthetic 
method and, approaching the divisions of our subject according 
to the relative simplicity of the processes which they involve, 
discuss: 1, Conception; 2, Judgment; 3, Reasoning. This 
course we shall adopt. See Thomson, § 41. 

9 : b. Are Conception, Judgment and Reasoning 
independent processes, or mutually related ? 

It should, in this connection, be borne in mind that Concep- 
tion, Judgment and Reasoning are not strictly independent 
processes; but, wi in reality, only various applications of the 
same simple faculty, that of comparison" (Hamilton, p. 194) ; 
and that " concepts, judgments and reasonings fall into 
different classes, as the act — and consequently the result of 
the act — is of a greater or less simplicity." Hamilton, p. 83 ; 
ef. Atwater, p. 83 sq. 



10. State the four Fundamental Principles which 
underlie the Laws of Thought. 

These principles serve merely to test the formal correctness 
of our thinking— its self consistency. Our thinking limy be 
correct in form, yet not true in matter; but it cannot be 
materially true unle>s it is formally correct. See Thomson, 
p. 250 : Bowen^ p. 42. 



18 OUTLINES OF LOGIC. 

The principles referred to are : 

I. " The Principle of Identity, which expresses the relation 
of total sameness in which a concept stands to all, and the 
relation of partial sameness in Avhich it stands to each, of its 
constituent parts. Its formula is A=A." Hamilton, p. 57. 

The formula may also be stated : A = (Ai\ ; A __. A. 

4 4 

To illustrate the importance of this principle : Leibnitz 
says, "The geometrician proceeds from hypothesis to hypo- 
thesis ; and, while the thought assumes a thousand different 
forms, it is still but by an incessant repetition of the principle 
4 the same is the same/ that he, performs all his wonders." 
Condillac sa}s, " Equations, propositions, judgments, are, at 
bottom, the same ; and, consequently, the reasoning process 
is the same in every science." Of. Everett, Science of 
'Thought, p. 102. 

Scholia, (a) Unless a thing be equal to itself — that is, 
maintain its essential identity — there can be no such thing as 
thought, (b) Things that are equal to the same thing are 
equal to each other, e.g. A=B, B = C, therefore A = C. 
(c) What is affirmed, or denied, of a whole, may be affirmed, 
or denied, of its parts, e. g. Man is a rational animal ; John 
is a man ; therefore John is a rational animal. 

II. The principle of Non-Contradiction. Aristotle's state- 
ment is: "The same attribute cannot be at the same time 
affirmed and denied of the same object." That is : a thing 
cannot be, at the same time, A and not-A — a diagram cannot 
be, at the same time, square and not-square. Kant's state- 
ment is : "The attribute cannot be contradictory of the object." 
e. g. A triangle cannot be round. The formula for this law is 
A — A = 0. e.g. Let A represent "two straight lines in 
the same plane which, however protracted, will never meet." 
You are required to think of those lines as meeting. The 
result is A — A = 0, the negation of thought. 

III. The Principle of Excluded Middle; that is: Of two 



OUTLINES OF LOGIC. 19 

contradictories, one or the other must be true — there is no 
middle course. Examples of contradictories are : 

No X is any Y ; 
Some X is some Y. 
The table is square ; 
The table is not-square. 

The table must, of course, be either square or not-square. 

Besides contradictory opposition, Logic recognizes contrary 
opposition ; in which both judgments cannot be true, but they 
may both be false. For instance : 

No X is any Y ; 

All X is all Y. 

The table is square ; 

The table is round. 

In these cases of opposition the judgments cannot both be 
true, but they may both be false. The truth may be : 

All X is some Y. 
The table is oblong. 

IV". The Principle of Sufficient Reason; that is: "What- 
ever exists must have a sufficient reason why it is as it is 
and not otherwise." Leibnitz. 

10 : a. What distinction is to be made between 
" reason and consequent " and " cause and 
.effect" ? 

1>\ reason and consequent we do not mean cause and affect; 
though cause and effect stand to each other in the relation of 
reason and consequent. Reason and consequent have relation 
to the form of thought — the necessary sequence of ideas ; 
cause and effect, to the matter of thought — the necessary 
sequence of real existences. wt A cause is something which 
not only precedes, but has power to produce the effect." 
Fleming. Cf. Thomson, p. 1 18. What is meant by the fourth 
law is : Reason and consequent are correlative. When a 
reason exists, there must be a consequent; and vice versa. 



20 OUTLINES OF LOGIC. 

When 110 reason exists, there can be no consequent : and 
versa. Granting the reason, we must grant its legitimate 
consequent. Denying the consequent, we must deny its legi- 
timate reason. But admitting a consequent does not neces- 
sarily admit the reason assigned. Contrast: "If it has rained, 
the ground is wet/' with " If the mercury falls below 32 , ice 
is formed/' In the former case, to affirm the consequent does 
not affirm its antecedent (since other causes may produce the 
same effect) ; in the latter case to affirm the consequent 
(though it is merely a consequent — not an effect) does affirm 
the antecedent ; for the two are inseparably connected. See 
Thomson, pp. 227-30, on this subject. Also Fleming, p. 78. 

10: b. Does the fourth principle stand on the same 
footing as the other three ? 

The last law stands on quite a different footing from the 
other three, which are really but different phases of the same 
principle. It is frequently regarded as falling within the 
province of Metaplrysics rather than Logic, in which case 
fct reason and consequent" are confounded with tc cause and 
effect." The fourth law, as the basis of the conditional 
syllogism, seems properly to belong to Logic ; although it 
occupies a position subordinate to the other three, and might. 
conceivably, be dispensed with. 

In regard to the first three laws, Hamilton says: "What- 
ever violates the laws whether of identity, of contradiction 
or of excluded middle, Ave feel to be absolutely impossible, 
not only in thought but in existence. Thus, we cannot attri- 
bute even to Omnipotence the power of making a thing 
different from itself, of making a thing at once to be and not 
to be, of making a thing neither to be or not to be." Logic, 
p. 70. On this conditioning of Omnipotence, see Jftutsel, 
p. 77. 



11. What do you understand by Conception; what by 
an intuition ; what by a concept ? 

Conception (con and capere) is that power, or process, ol 
the discursive faculties by which several intuitions of individ- 
ual objects are combined into a general motion. 

By an " intuition" (in and tueri) we understand an iin- 



OUTLINES OF LOQIG. 21 

mediate, face-to-face presentation of an external object or an 
Internal state. 

l>y a " concept" {conceptum = what is conceived) we 
understand, the general notion at which we arrive as the 

result of the process of conception. Cf. Thomson, $ 47. 

1 1 is a convenient, and is coming to be a very general, 
custom to use the term "conception" to designate the process 
of forming general notions ; the term " concept," to designate 
the general notion, which results from that process. " Per- 
ception" and " percept" are used (thongli not so widely) with 
a similar discrimination. 



11 : a. Explain and illustrate the method of forming 
concepts. 

(1) There must be placed before the mind several repre- 
sentations of essentially similar, but, in some respects, differ- 
ent, objects, e.g. Several books — one, a logic; another, a 
history - one, in English ; another, in Latin — one, in cloth ; 
another, in leather — one, in 4to ; another, in 12mo — one, 
costing 25 cents ; another, $5.00 ; etc., etc. 

(2) The mind must reflect upon the characteristics of these 
different objects — carefully discriminating what is common to 
all, and necessary to constitute each '' a book," from what is 
accidental or exceptional in any given case (as, for example : 
the object-matter, the language, the binding, the size, the 
expense, etc., etc.). 

(3) The mind must withdraw its attention from that which 
is accidental and peculiar in the objects before it ; and lix its 
attention on that which is essential and common. This is a 
P-\ etiological statement of the next step in the process. See 
Mansel, p. 37 sq. Logically speaking, the mind abstracts, 
or draws off, the essential from the accidental qualities of the 
objects before it — those qualities which belong to all the 
objects, from those which belong to only some of them. In 



22 OUTLINES OF LOGIC. 

the case before us, the essential qualities are : (a) printed 
leaves ; (b) substantially fastened together. 

(4) The mind extends its notion of an object which 
(whatever else it may possess) possesses the essential 
qualities noted, to a class. It generalizes the results of its 
observation and reflection. It conceives of something which 
is not tills book, that book, or the other book ; but book in 
the widest sense of the term — including all books that ever 
have been or ever will be. 

If our general notion be formed from an inspection of an 
insufficient number of individual presentations, it will soon 
need revision — as, for instance, in the case which we have 
chosen for illustration, the first time one comes in contact 
with " a blank book." The way in which our general notions 
are extended and modified by increased observation and 
reflection is well illustrated by Thomson, Laws of Thought, 
§ 48. 

% (5) The mind gives to the general notion thus formed, a 
name by which it can identify and recall it — generally the 
same name which it had been accustomed to apply, in a 
narrower sense, to the first object of this kind with which it 
was acquainted. 

While the process of Conception may be analyzed into the 
five different stages already discriminated, — which are known 
as Comparison, Reflection, Abstraction, Generalization and 
Denomination, — it should be borne in mind that, practically, 
the process is so rapid, or so far beneath consciousness, as 
generally to set at nought all attempts at analysis ; and that 
the different steps which have been indicated are not inde- 
pendent processes ; but, in reality, one process. 

An extra-Logical problem here suggests itself which pos- 
sesses no little interest. Does not the man whom Thomson 
introduces (p. 94), start with the general notion " sea;" and 
is not the process one of clarification? Does he not, at least, 
set out with the idea that a general notion is possible? If so, 
where does he get that idea? Does the particular always pre- 



0UTLINB8 OF LOGIC. - 2:5 

cede the universal? See Mansel, p, II Bq. ; Hamilton, 
Lectures on Metaphysics, pp. 492-501. 



11 : b. Why is Denomination regarded as essential 
to the process of conception P 

Denomination is regarded as essential to the process of 
forming a concept, because, without giving names to our 
general notions, it is impossible to retain, identify and impart 
them. They evaporate like an uncorked volatile odor. See 
At irater, p. 54. There is an objective existence whose mental 
reproduction helps us to recall and identify the individual 
presentation ; but nothing in nature corresponds to the general 
notion. Hence, without some note or symbol, it could not be 
retained or recognized. The name is to the concept, accord- 
ing to Hamilton, Logic, p. 98, as a fortress is to a subjugated 
country ; or the arch-way to an excavated tunnel. It helps 
us to hold what the activit}' of thought has already secured. 

12. State the threefold question respecting the relation 
of thought to language ; and indicate the answers which 
you would trive. 

The question respecting the relation of thought to language 
is threefold : 

(1) Are language and thought identical ? Does language 
correspond to thought as the raised figure on embossed paper 
corresponds to the depression caused by the stamp on the 
other side? Are the two co-ordinate, standing in the same 
relation to the human mind — the stamp? Is their corres- 
pondence necessary, absolute and universal? If so: we may 
found an analysis of the reasoning powers on an examination 
of language, rather than thought, if more convenient. See 
Ever of TfiougJd, p. 66 sq. Yet Whately is 

idly belabored by Hamilton {passim) for treating of 
language rather than thought. 

(2) Discriminating between thought and language, Is 
thought possible witlioid articulate speech as its instrument t 

i Is thought possible without some * f >rt of language as its 



24 * OUTLINES OF LOGIC. 

instrument ? Do babes think ? Do the brutes ? Do the 
untrained deaf and dumb? 

On these questions, see Thomson, §§ 27, 28 ; Mansel, p. 26 
sq. ; Whately, g 5 and note ; Dictionnaire de Lingwistique, 
p. 167 sq. and notes to pp. 118, 139. Per contra, see 
M'Cosh, Logic, p. 64 sq., and Whitney, Language and the 
Study of Language, p. 403 sq. 

12: a In what senses are the words "thought" and 
" language " to be used in this discussion ? 

In discussing these questions, it must be borne in mind that 
the word ^ thought" is used in the restricted sense already 
indicated; while " language" is not to be confined to articu- 
late speech, but covers an}^ method of communicating, or 
s}'mbolizing, thought. See Thomson, §18 and note. 

Failure to arrive at a correct understanding of the relation 
of thought to language, arises, almost invariably, from mis- 
apprehension of these terms. Giving to u thought" and 
ic language" the meaning above indicated, it would seem to 
be indisputable that there can be no thought without 
language. 

13. Explain Leibnitz's distinction between notative 
and symbolic terms ; and show its bearing on the ques- 
tion respecting the relation of thought to language. 

When an object presented to the mind is so simple that we 
apprehend, at a glance, its essential qualities (and give it a 
name which indicates them), we are said to have an intuitive 
knowledge of the object and the term hy which we charac- 
terize, it is called notative. When the object is so complex 
that we do not apprehend, at a glance, its essential qualities, 
our apprehension of the object is said to be symbolic, and the 
term by which w r e characterize, it is called symbolic. 
Frequently, a s}'mbolic and a notative term for the same 
object are combined in one sentence. e.g. "Rochester 
(symbolic) is a city of 80,000 inhabitants, situated on the 
Genesee river, six miles from Lake Ontario (notative) ." 

For the distinction here indicated, we are indebted to 
Leibnitz, for whose original statement see Mansel Prolog. 
Log. p. 37 note, and Baynes, Port Royal Logic, p. 123 sq. 
Cf. Thomson, § 25; Hamilton, p. 128; Atwater, p. 07; 
Jevons, pp. f)7-G0. 



OUTLINES OF LOGIC. 25 

The words in a language cannot be absolutely classified as 
"notatiye" or "symbolic." The same word may be a 
"symbol" to one man, while to another man, of greater 
mental acuteness and larger attainments, it is a "note." The 
same word may be, to the same man, at one time a " note" 
and, at another, a " symbol," according to the degree of his 
mental activity and his opportunity to explicate his thought. 
There are many words, however, (as, for example, " state," 
" society") which denote objects so complex that they may 
be regarded as used symbolically b} T the entire race. Such 
words pass from mouth to mouth, without our stopping to 
explicate their value, or attaching to them any precise and 
definite meaning, just as a dollar passes from hand to hand, 
without our stopping to think that it is made up of a thousand 
mills. Unquestionably, much of our speech and nearly all of 
our thinking involve very largely the S3 T mbolic use of terms. 
When we claim that language is essential to thought, there- 
fore, it is not intended to assert that all the discursive pro- 
cesses are fully drawn out in words to which a sharp and 
definite meaning is attached. 



13 : a What advantage, and what disadvantages, 
arise from this symbolic use of terms ? 

The advantage is that, like the use of signs in an Algebraic 
process, it greatly abbreviates and facilitates the processes of 
thought. Much of our thinking is thus carried on in a sort of 
mental shorthand. 

The disadvantages arise from the fact that we frequently 
use terms sj-mbolically without being able, on demand, to 
explicate their meaning — that is : we suppose ourselves to be 
thinking, when we have, in reality, no clear and definite 
thought. 

See M'Cosh, Lor/ic, p. 70 sq. ; Bowen, Logic, p. 24 sq. ; 
Hansel, p. 36. 

14. What views have been held respecting the exist- 
ence of realities which correspond to general terms ; 
and which view are you inclined to adopt? 

The controversy between the "nominalists" and the 
" realists," which was carried on with intense feeling during 



26 OUTLINES OF LOGIC. 

the scholastic age (not only from its philosophical significance, 
but from its bearing on certain grave theological questions — 
see Bain's Mental Science, Am. ed. Append, p. 24) had refer- 
ence to the existence, or non-existence, of realities correspond- 
ing to the general terms which result from the process of 
conception. The question was, for instance: " Is there an 
existence which corresponds to the general term man, alto- 
gether apart from any- particular man — any individual member 
of the human family?" The " realist," following out Plato's 
doctrine of ideas [See Republic, B. 7, Ch. 1], answered: 
"Yes, there is, outside of the human mind, a real existence, 
which corresponds to every general notion. 'Universals' 
exist apart from, and independent of, 'particulars' — apart, 
also, from the mind that apprehends them." The " nomi- 
nalist," following out the suggestions of Aristotle, answered: 
" No. The universal exists only in the particular. The 
general term is a mere name to which no objective reality 
corresponds — a convenient designation for individual objects 
which possess similar attributes." Among both "realists" 
and " nominalists," there were, of course, various shades of 
opinion. Ultraists in either direction are rarely met with at 
the present day. Thinkers of the school of Comte, J. S. Mill 
and Herbert Spencer are avowed, and tolerabl} T pronounced, 
"nominalists." Avowed "realists" are more rarely met; 
though there is still much latent "realism" — especially in 
Theological circles. See Garden, Outlines of Logic, p. 153, 
who insists the " realism" is divinely inculcated. 

The position most frequently taken, at the present time, 
respecting the existence of " universals," is that of the 
" conceptualist," who, holding middle ground between the 
" realist" and the " nominalist," affirms the existence in the 
mind, but not apart from the mind, of realities corresponding 
to general terms. That is : the " conceptualist" concedes that, 
objectively, the universal exists only in the particular ; but 
claims that, subjectively, it has independent existence in the 
mind of man. In the divine mind, as well as the human, 
according to most " conceptualists." For example, the 
general notion " vertebrate animal" existed in the mind of 
God before the creation of the animal kingdom. See 
Thomson, p. 117, and Agassiz, /Structure of Animal Life, 
p. 117. The general notion triangle exists in the mind of 
man, as a concept generalized from individual objects, alto- 
gether apart from any particular triangle. This the " con- 



OUTLINES Ol^ LOU 10. 27 

V 

ceptualist" of to-day affirms, but the " nominalist" denies. 
To the question : wt Is it possible to conceive of a triangle 
which is neither equilateral, rectangular, nor scalene, but all 
these ut once?" the " conceptualist " answers, "Yes;" the 
kk nominalist" answers, " No." It is certain that the general 
notion triangle cannot be objectized — that no image, or 
picture, of the universal triangle can be formed. This is, 
probably, what the fct nominalist" means by saying that the 
concept triangle has no real existence. But is the formation 
of a mental image of the universal triangle essential to the 
existence of the concept. May we not think triangularity , 
holding in abeyance the qualities and proportions of the sides 
and angles? May not the mind grasp, at the same time, the 
notions of triangles equilateral, rectangular and scalene, so as 
to gain from their contemplation a general notion of all that is 
common to each — as the eye, glancing at a handful of cherries, 
takes in no one cherry in particular, but all at once ? Or does 
the mind, passing, with incredible rapidity, from one notion to 
another, seem to take in all at once, while its receptivity is, 
in reality, successive? See James Mill, as quoted in the 
appendix to Bain's Mental Science, Amer. ed. p. 31. 

In many cases, doubtless, the mind objectizes the general 
notion triangle by the image of that particular triangle with 
which it is most familiar, maintaining a mental protest that 
the image is inadequate to its purpose. But is this always so? 
And does not the mind's conscious protest in such a case 
attest the existence of a general notion which, we have freely 
conceded, cannot be objectized ? 

In favor of " conceptualism," as opposed to " nominalism," 
we may allege the tendency of men of different ages and 
different nations to form the same concepts — a point which is 
well stated by Thomson, Laws of Thought, p. 117. With 
reference to " realism" (which is regarded by philosophers of 
the present day as an exploded notion, with which even the 
philosopher from whom it was derived was never more than 
half satisfied) the following questions ma} r not be im- 
pertinent : 

(1) What evidence have we of the existence of objective 
realities corresponding to general terms ? 

(2) What is gained by their recognition ? As Occam says : 
Entia non sunt multiplicanda praettr necessitatem, 

(3) Precisely what are they? 

(4) Just where are they? 



28 OUTLINES OF LOGIC. 

(5) How do these "universals — conceding their existence- 
influence and modify the individuals of which they are the 
t} T pes? What, for instance, is the tangible connection of the 
universal, archetypal, man with John Doe and Richard Roe? 

On this general subject, the following works may be con- 
sulted. Thomson, pp. 116-126; Hamilton, Logic, pp. 91, 
97, Metaphysics, pp. 476-492 ; Schwegler, Hist, of Phil., 
p. 100; Mill, J. S., Logic, p. 117 sq. Amer. ed. ; Bain, 
Mental Science, pp. 176 sq. and appendix, Deductive Logic, 
pp. 5-6 ; Garden, Outlines of Logic, appendix. 



15. Define genus, species, individual, differentia, 
essence, mark. Classify marks. 

Genus may be defined as : (1) a class of objects, (2) 
associated together upon the basis of essential similarity, and 
(3) susceptible of subdivision into classes. 

Species are the subordinate classes into which a genus is 
divided. 

An individual {in-dividere) is that which cannot be divided 
without ceasing to be what it is — as, for instance, a sword, a 
man. The individual is the unit out of which subordinate 
classes are formed. When a class is divided, its separate 
members can bear the name of the class. When an individual 
is divided, its separate parts cannot bear its name. 

Differentia my be defined as the attribute, or attributes, 
which distinguish an individual, or a class, from the class to 
which it belongs, e. g. Rationality differentiates man from 
the class animals. 

Essence {essentia, root esse) is that in which the very being 
of a thing resides — that which constitutes it what is. 
Ld per quod res est, et id est, quod est. 

By marks we are to understand : those attributes or quali- 
ties by which we recognize an object, and assign it to its 
appropriate class. 

Marks are to be divided into essential — which always 



01 i um - 01 LOOK . 29 

accompany an object; and accidental — which may, or may 
not. accompany it. 

They are also to be divided into: contradictory — which are 
opposed to each other in the very form of expression, as 
•• sweet' 1 and " not-sweet," *• wise" and "unwise" ; repugnant 
(better, •• contrary") — which arc opposed to each other in 
matter, but not in form, as u sweet" and u sour," "wise" 
and % * foolish" ; and compatible — between which no opposition 
its. 

For further classification under the head of u marks," see 
Bowen, Logic, p. 02. 



16. Explain the distinction between obscure and clear, 
confnsed and distinct, inadequate and adequate pres- 
entations. 

By a w - presentation" we mean the impression which any 
object makes upon the mind. Sometimes these impressions 
are made without being noticed at the time. For instance, a 
clock strikes while we are busy at study. We do not notice it 
at the time ; but, afterwards, knowing that it must have 
struck, we dimly recollect hearing it. These unrecognized 
presentations are called, in Logical nomenclature, "obscure," 
in opposition to those recognized presentations — called 
•• clear" — with which alone Logic has to do. 

Clear presentations, or " cognitions," are subdivided into 
•• confused'' and " distinct." When we clearly recognize a 
thing, but cannot tell how we recognize it — e. g. the color red 
— our presentation of it is said to be Cw confused" ; when we 
can give the marks by which we recognize it, our presentation 
of it is said to be *• distinct." 

if we can go still farther, and explain the marks which we 
have just given — or. " give the marks of the marks" — our 
sentation is said to be •■ adequate" ; if not, it is said to be 
• k inadequate." 



30 OUTLINES OF LOGIC. 

There are, of course, various degrees of adequac}'. Indeed, 
clearness, distinctness and adequacy are, in themselves, but 
different degrees of the same general faculty, cognition. See 
Hamilton (who is especially happy in treating this subject) 
Logic, pp. 112-118. Also, Thomson, §46; Jevons, p. 53, 
sq. ; Baynes, Port Royal Logic, p. 423 sq. 

17. Define summum genus, infima species, subaltern 
genus and species, proximate genus and species, co- 
ordinate and disparate species. 

Summum genus is the highest class that we recognize in a 
connected system of classification ; infima species, the lowest. 
All between, are subaltern genera and species — genera to the 
class below, and species to the class above. Proximate genus 
is the class next above a given class in a connected system of 
classification ; proximate species, the class next below a given 
class. Co-ordinate species are species belonging to the same 
genus ; disparate species {dispar, unequal) are species belong- 
ing to different genera. 



18. What is meant by Extension and Intension, and 
what is their reciprocal relation ? 

The " extension" of a concept (ex-tendere) is its capacity to 
denote objects. The more objects it includes, the greater its 
extension. The " intension*' of a concept (in-tendere) is its 
capacity to connote marks. The more qualities or attributes 
it suggests, -the greater its intension. Extension and in- 
tension stand to each other in reciprocal relations. As the 
extension of a concept increases (i. e. as it is made to include 
more objects) its intension diminishes (i. e. it indicates fewer 
qualities) ; and vice versa. The extension of the word 
" plant," for instance, is great — it includes objects almost 
innumerable, from the lichen to the oak ; but it suggests few 



OUTLINES OK LOGIO. 31 

qualities save that of vegetable life. Its intension is small. 
"Geranium," on the contrary, covers comparatively few 
objects, but many qualities. Its intension greatly exceeds its 
extension. See Jevons, p. o7 sq. 



18 : a. Explain the distinction between denotative 
and connotative terms. 

On denotative and connotative terms, see W /lately, B. 2, 
eh. 5, § 1 ; Mill, B. 1, ch. 2, § 5 ; Atwater, p. 46. 

Bowen, Logic, p. 59, says : " It is a convenient use of lan- 
guage, though the words are sometimes used in another 
manner, to say that a word, or name, connotes the marks 
which make up its significance, and denotes the individual 
objects which make up these attributes." Fowler, Deductive 
Logic, p. 19, says: "A term is said to denote individuals, or 
groups of individuals ; and connote attributes, or groups of 
attributes." This is the ordinary usage, simply because most 
terms have reference primarily to objects, and only secondarily 
to attributes. That to which a term has primary reference, it 
is said to denote ; that to which it has secondary reference, it 
is said to connote \_cum-notare~\. 

18: b. Illustrate the fact that every judgment may 
be read in the whole of extension, or the 
whole of intension. 

The whole of extension alone was regarded as a " Logical 
whole" by the followers of Aristotle, who claimed that judg- 
ment consisted in referring individual objects to the class of 
objects to which they belonged. 

By applying to a concept the term " Logical whole," the 
Aristotelian meant to deny its objective existence — to charac- 
terize it as merely a creation of the mind. The u whole of 
intension" he regarded as a iC Metaphysical whole," which had 
objective and real existence. See Thomson, p. 101, note. 
Also, Fleming, who says: " Logically, the species is in the 
genus; Metaphysical^, the genus is in the species." That is: 
so far as our conceptions are concerned, the individual, or the 
lower class, exists in the class above it ; so far as actual 



32 OUTLINES OF LOGIC. 

existence is concerned, the higher class exists only in the 
lower, the lower only in the individual. 

Hamilton claims — and, justly — that we may refer individual 
attributes to an intensive whole just as readily as individual 
objects to an extensive whole. Hence, that the whole of 
intension is just as Logical as the whole of extension. 
According to Hamilton, every judgment may be read either 
in the whole of extension or the whole of intension. Thus, 
Man is mortal, may mean either: " Man is one of the class 
of beings possessing mortality" — (extension); or, it may 
mean : u The quality of mortality is one of those qualities 
which inhere in man" — {intension). See the author's A rt of 
Expression^ p. 39. 

See Mansel' s Aldrich, p. 46 note, on the methods of ex- 
pressing this two-fold relation, which were available to the 
Greeks. 



18: c Explain how the subject can be in the predi- 
cate, and the predicate, at the same time, 
in the subject. 

If we read a judgment in the whole of extension, the subject 
is in the predicate ; since the predicate covers more objects 
than the subject. If we read a judgment in the whole of 
intension, the predicate is in the subject ; since the subject 
covers more attributes than the predicate. See Thomson, 
% 52 ; Atwater, p. 55. 

To illustrate : the " extension" of the term jylant, is large ; 
its " intension," small. The term geranium precisely re- 
verses these conditions. Using 
a heavy line for extension ; a 
light line for intension, the fol- 
lowing diagram will illustrate 
this point : 





-(0 



OUTLINES OF LCMJIC. 



33 




It will be seen that, so far as extension is concerned, the 
subject (geranium) is easily included in the 
predicate (plant). The geranium does, in fact, 
belong to the class of objects which "plant" 
denotes. Hence we have : G is in P. 

With reference to intension, on the other hand, the predi- 
cate (plant) is easily included in the subject (geranium). The 
qualities of the plant (vegetable life) are, in fact, 
only found in combination with other qualities, 
such as distinctively characterize the geranium, 
the fern, the lichen, the oak, etc., etc. Hence 
we have : P is in G. 




19. Give Thomson's " Scheme of Conceptions in the 
three wholes of Extension, Intension and Denomination." 

We give from Thomson, Laics of Thought, p. 100, with 
some modification, the following table, which is designed to 
illustrate the meaning of the terms summum genus, subaltern 
genus, infima species ; and also to show that as extension 
decreases from summum genus to infima species, intension 
increases, and vice versa. 

Class. Denomination. Intension. Extension. 

Summum Genus 

'tern Genua 



Infima &p< 



Body Matter with form v. Stone, plant, brute, man 

Living Body M " " and life ^ Plant, brute, man 

Aninial " " M •« an d sensation N 

^ an " " " ■' " M and reason \ Man 



The table serves also to illustrate the fact that summum 
genus and infima species are not absolutely fixed, but are 
simply the highest and lowest classes at any time recognized. 
Thus, we might recognize "matter" as a genus higher than 
the highest which Thomson recognizes : and " man," instead 
of being infima species, might be a subaltern genus subdivided 
into Caucasian and non-Caucasian. In a treatise on Zoology, 



34 OUTLINES OF LOGIC. 

u animal," one of Thomson's subaltern genera, would be 
summum genus. In a treatise on Ethnology, "man," 
Thomson's In fit mi species, would be stunminu (joins. 

20. Explain the distinction between positive and 
privative concepts. 

Positive concepts have substantial existence, and result 
from the generalization of the essential attributes which 
certain objects possess. Every positive implies a correspond- 
ing privative, which, in its origin at least, is the formal 
negation of its positive. Thus the positive concept " man" 
implies the privative concept " not- man" ; the positive 
" kindness," its privative " unkindness." Though the 
privative concept is originally the mere negation of its 
positive, it may come to have, — as in the case of the term 
" unkindness," — an independent existence. See 'Thomson, 
pp. 106-7. When we meet the term " unkindness," we do 
nofc first think of " kindness" and then negative our concep- 
tion. The term has acquired a substantial meaning of its 
own— something midway between " kindness" and " cruelty." 

20 : a. What do you understand by the second 
sphere of the privative ? 

Every pair of positives and privatives divides between them 
the universe. Everything that exists is — for instance — either 
square or not-square. It is absurd, however, to think of the 
atmosphere as not-square— which it, doubtless, is— since we 
could not reasonably regard it as having any form. While 
the universe, then, is the first sphere of the privative, we 
recognize a second sphere of the privative in that department 
of being where the qualities of the positive might reasonably 
be expected. Thus, " the universe" would be the first sphere, 
i 'bodies" (or matter with form) the second sphere, of 
" square " and " not-square." 



OUTLINES OF LOGIC. 35 

Emphasizing the importance of the distinction between 
positive and privative concepts, Thomson, Laws of Thought, 
p. 113, Bays : 

*• Private conceptions not only afford the means of varying 
the forms of thinking, by furnishing for every affirmative 

judgment, equivalent negatives, and for every negative, 
affirmatives ; but they enter into and assist the higher pro- 
cesses of the reason in all that it can know of the absolute and 
the infinite. To attribute the properties of one or many 
individuals to every other of the same class is within the reach 
of the mere understanding, and the brute creation enjoy some 
share of it ; but from the seen to realize an unseen world, not 
by extending to the latter the properties of the former, but by 
assigning it attributes entirely opposite, is a prerogative of 
reason alone." 

His statement is based {ad finem) on the Kantian distinc- 
tion between the sphere of the understanding and that of the 
reason — the former being coincident w T ith the sensuous, the 
latter with the super-sensuous world. 



21. What do you understand by Logical Division; and 
what are the principles upon which it must proceed ? 

" Logical Division is the enumeration of the various 
coordinate species of which a proximate genus is composed." 
Thomson, § 55. Cf. Jevons, p. 105 sq. It must proceed 
in accordance w T ith the following principles : 

1. The division must be made, throughout, upon one basis 
of division. Thus, if we have begun to classify man on the 
basis of color, w r e must adhere, rigidly, to that basis of 
classification. If we violate this principle, we shall be likefy 
to violate both the principles which follow. 

2. The dividing members must exclude each other — that is, 
nothing must be included in one division which is also in- 
cluded in another division. 

3. The dividing members must be equal, taken together, to 
the thing to be divided — a principle which simply requires that 
our task be carried to completion. 



36 OUTLINES OF LOGIC. 

Care is also necessary that the divisions which we enumerate 
are strictly coordinate. As Thomson sa}-s : "A division 
where the species are not coordinate, although correct in other 
respects, would offer a bad arrangement for purposes of 
science ; thus, sciences should not be divided by a reader of 
Aristotle into ' Theoretical and practical, together with 
Poetry, Rhetoric, and Dialectic,' because the first two are 
divisions, and the last three are subdivisions of a genus that 
has been omitted, namely, the Poetic Sciences. " Laws of 
Thought, p. 106. 

This defect is especially common in Rhetorical Division, 
which is essentially similar to Logical Division, both in its 
nature and in the principles by which it is governed. 



21 : a. What significance is there in the statement of 
the scholastic Logicians f Divisio debet esse 
bimembris ? 

The bimembral division — or the division of a concept into 
two members, a positive and its corresponding privative, e. g. 
animal into vertebrate and invertebrate — is the only one w r hich 
Pure Logic, in strictness, recognizes ; being the only one 
which is a priori, having to do with the form and not the 
matter of thought. From one point of view, however, this 
division is practically useless, since we know nothing about 
the larger of the dividing members, save that it lacks the 
marks of the smaller. The bimembral, or dickotj-mous, divi- 
sion is, however, practically useful as a test of the thorough- 
ness with which the principles of division have been applied 
in any given case. When our division conforms accurately 
to these principles, an} r one of the dividing members may be 
taken as a positive, and all the others grouped as its corres- 
ponding privative. But when we attempt this bi-membral 



OUTLINES OF LOGIC. 37 

reduction, our attention is frequently called to the fact that 
the members which we seek to reduce to A and not-A have 
not been formed in accordance with the principles of Division. 

For example : If I have correctly classified a library on the; 
topical basis, its various departments may be reduced to two 
— Poetry and not-Poetry. Now suppose that, thinking an 
original copy of Homer of more interest to the classical 
student than the student of poetry, I have put Homer in the 
department of Classical Literature. The moment I apply the 
bimembral test to my classification, Homer's works appear in 
the department of not-Poetiy, and I am reminded that I have 
not proceeded throughout my task, upon one principle of 
division. If, from similar considerations, I have assigned 
Homer both to the department of Poetry and to the depart- 
ment of Classical Literature,' the bimembral test shows that I 
regard Homer's works as both Poetry and not-Poetry. That 
is, that my dividing members do not exclude each other ; and 
that their sum will exceed the object to be divided. 

This bimembral test is of very great practical advantage in 
Rhetoric. It is wise to go carefully over your material before 
beginning to write, making each head, in turn, a positive, 
and grouping all the others to form the corresponding 
privative. 

22. What do you understand by Logical Definition, 
and what are the principles upon which it must proceed ? 

1. Logical Definition (defl.nire, to fix the 
s or boundaries) consists, strictly 
speaking, in giving the genus and differ- M = 
entia of a species. e. g. Man is a 
rational animal. 

Hence, neither the summum genus nor the individual can, 
in Logical strictness, be defined. The individual may, how- 
ever, be differentiated by some accidental mark from the 
infima species, in accordance with the method by which the 
species is differentiated from the genus — as when we say : 
James Madison was the fourth president of the U. S. 

Here the term " president of the U. S." does not indicate 

4 




38 OUTLINES OF LOGIC. 

a genus, and the attribute "fourth" is not sufficient^ 
essential to constitute a " specific difference" ; yet the method 
is jwtctically that of Logical definition in its strict sense. 

2. The term "definition" is more loosety used to denote the 
process of giving some mark, or combination of marks, which 
may serve to identify or explain the object to be defined. 
Thus Cicero, in the De Oratore, says: "Definition is some 
brief and circumscribed explication of those things [attributes] 
which characterize the thing [object] that we wish to 
describe." 

This lower grade of definition (which is sometimes called 
Rhetorical Definition) must proceed in conformitj' with the 
following rules : 

(1) The marks enumerated to define the object must be, so 
far as possible, essential. 

(2) The definition must be precisely adequate to the thing 
to be defined — neither too broad, nor too narrow. Thus: 
"Words are the signs of thought" is too broad ; since other 
things are the signs of thought. Again: "Words are the 
articulate signs by which an orator expresses his thought" 
is too narrow. There should be no limitation to the orator. 

(3) The definition should not contain the name of the 
object to be defined, or a synonym of that name. "Life is 
the sum of the vital forces" is, for example, a definition 
which does not largely increase our knowledge. 

(4) The definition must be couched in clear and un- 
ambiguous language. Pres. Porter's definition of happiness 
as "The ecstatic equilibrium of the constituents of conscious- 
ness," is defective just here. 

(5) The definition must not be negative when it can be 
positive. 

3. Using the term " definition" still more loosely, we may 
accept as definition an}' process which helps one to identify or 



OUTLINES OF LOGIC. 3 ( J 

apprehend the object to be defined. Thus, we have definition 
by enumeration of the constituent parts of an object— as when 
1 >ay (giving no marks, whatever): "The New England 

States are Me., N. II.. Yt., Mass., R. I., Conn."; by the 
substitution of names — as when I say: "Efflorescence means 
blossoming out" ; by the substitution of narrative phrases — as 
when I say: U H 2 is the symbol that chemists make use of 
to designate water"; etc., etc. See Thomson, £S 70, 71; 
At water, p. 79. 

Division and definition are correlative processes. Each 
-ts the other. Each implies the other. Though differing 
utially in their nature, the two processes go on at the 
same time. See Thomson, p. 108 ; Ativater, p. 81. 

Hamilton refers the entire subject of definition to Applied 
Logic, on the ground that it requires us to take cognizance of 
the matter, no less than the form, of thought. Thomson 
discusses it under Conception, p. 107 sq., under Judgment, 
p. 138 and p. 142 sq., and, also, under Applied Logic, p. 269 
sq. — a fact which seems to vindicate Hamilton's course. 
Logical Definition, in the strict sense of the term, is certainly 
not out of place under Pure Logic, however, and we have 
preferred to say all that we have to say respecting definition 
here. On the distinction between nominal and real definition, 
see Fleming, p. 128 ; Hamilton, p. 343. 

22 : a - Illustrate the fact that genus and differentia 
are really two concurrent genera. 

Instead of regarding the differentia as peculiar to the 
species defined (which it must be within the genus of which it 
cuts off a segment — else, there is no definition) : we may 
regard the differentia as itself a genus which serves to define 
an object by intersecting, or overlapping, another genus. 
Thus, instead of representing u Man is a rational animal" 
by the diagram 



M 




40 OUTLINES OF LOGIC. 

we may represent it by this diagram : 




Here, the distinction between genus and differentia van- 
ishes. Man is defined by the concurrence of two genera, 
and we may say that " animal " differentiates him from 
"rational," just as truly as that "rational" differentiates 
him from " animal." See Atwater, pp. 77-78 ; Hamilton, p. 
106 ; Thomson, p. 137. 

23. "What is meant by a Logical judgment; what by a 
proposition; what by the terms of a judgment? 

A Logical judgment is the mental affirmation of agreement 
or disagreement between two concepts, or an intuition and 
a concept. A proposition is a judgment expressed in words. 
The terms {termini, boundaries) of a judgment are the two 
notions compared ; the terms of a proposition are the subject 
and the predicate. 



23 : a. What is meant by primitive, or Psychological, 
as distinguished from Logical judgment ? 

Whenever an object is presented to our consciousness, we 
judge that it exists— we affirm its agreement with the concept 
existence. Judgments of this nature, which predicate of an 
object existence merel}' and are the result rather of intuition 
than of a process of thought, are called by Atwater, p. 53, 
"primitive"; by Mansel, p. 63 sq., " Psychological" 
judgments.' 

24. What is meant by the Quantity of a judgment; and 
how are judgments classified under this head ? 

By the Quantity of a judgment we mean, the extent to which 



OUTLINES OF LOGIC. 11 

its subject term is employed in predication. If the whole of 
the subject is employed — e. g. U AU men are mortal" — the 

judgment is said to he " universal ;" if hut a part of the 
subject is employed — e. g. "tioine men are rascals" — the judg- 
ment is said to be "particular." 

IS Singular" judgments, in which the subject is an indivi- 
dual — e.g. "This man is wealthy" — are also recognized ; but 
need not, for Logical purposes, be discriminated from " uni- 
versal" judgments, since they introduce the whole of the 
subject. •■ Indefinite," t; numerical" and " plurative" judg- 
ments are also recognized by some logicians. 



24 : (i- What view does Hamilton take of particular 
judgments ? 

Hamilton contends that particular judgments introduce the 
whole subject ; but that that subject is indeterminate or 
indefinite. For example : in the judgment " Some lakes have 
an outlet," he would regard the phrase " some lakes*' not as a 
part of the larger term u lakes" ; but as constituting a new 
term, the extension of which is undetermined, but the whole 
of which (whatever its extension may prove to be) is included 
in the affirmation. 

Hamilton's classification of judgments (see Logic, p. 171 
sq.) is as follows : 

f I Mental * 1- Determinate -jg-.^f-'- 
\ 2 ^Indeterminate- c . Particular. 



JUDGMENTS. <J 



rT T r , 7 (1. Fi- 
ll. Verbal. J % p] . 



eindesignate. [without signs] 



25. What is meant by the Quality of judgments; and 
how are judgments classified under this head ? 

By the Quality of a judgment, we understand the agreement, 
or disagreement, of its subject and predicate. With reference 
to quality, judgments are classified as •• affirmative" or 



42 OUTLINES OF LOGIC. 

" negative." In a negative judgment, the negation may 
directly modify the copula in expression, or it may not, — e. g. 
" This is not an animal"; " This is non-animal" ; "Not this 
is an animal," — but some negation must modify the copula in 
thought. It should be borne in mind that a proposition may 
embody a negative which does not modify the copula in 
thought, and, hence, leaves the judgment an affirmative one. 
e. g. "All that glitters, is not gold" — where the negative, 
though appparently modifying the copula, really modifies the 
subject. We must carefully discriminate between those judg- 
ments which are negative in 4 fact and those which are negative 
only in appearance. See Thomson, § 75. 



26. In what sense does Thomson use the word Rela- 
tion with reference to a judgment; and how are judg- 
ments classified with reference to Relation, using the 
word in this sense ? 

The Doctrine of Relation,— according to Thomson, § 68 
and § 73, first paragraph,- --merely takes cognizance of the 
question whether the predicate of a judgment is, or is not, 
coextensive with the Subject. Under this head judgments are 
classified as u substitutive" — in which the subject and predi- 
cate are coextensive, and can change places (e. g. " Sodium 
Chloride is common salt") ; and u attributive"— in which the 
subject and predicate are not coextensive, and cannot change 
places (e. g. '". Man is an animal"). 



26 : a. What is the ordinary use of the term 
Relation ? 

The Doctrine of Relation, as most logicians have employed 
that term, has reference to the discrimination of judgments 
into (i categorical " and " conditional" — terms which will be 
subsequently explained. 



OUTLINES OF LOGIC. 43 

27. Enumerate and explain the four predicable-classes 
recognized by Aristotle, and show how they may be 
reduced to two. 

According to Aristotle, every judgment indicates either the 
genus, or the property, or the definition, or an accident of its 
subject. Into one of these four classes, all predicates must 
fall. 

The genus always belongs to the subject; but belongs to 
other subjects as well. e. g. " Man is an animal" 

The property always belongs to the subject and to the 
subject only (that is, it is jwprius to it) without being the 
mark or attribute which we should choose to explain the very 
nature of the subject, e. g. " Man is afeatherless biped." 

The definition is the mark, or marks, which would explain 
the very nature of the subject, and, of course, belongs to the 
subject only. e. g. u Man is a rational animal. 

The accident is an attribute which may, or may not, belong- 
to the subject, and which belongs to other subjects as well. 
e. g. tw The nmi\ )§'' sick.'' 

Of these four classes of predicables, the definition and the 
property belong to the subject only ; and hence can change 
places with it. We may say w * a rational animal is man," just 
as truly as * k man is a rational animal." 

The genus and the accident do not belong to the subject 
5nly ; and hence cannot change places with it. To say that 
•• an animal is man," is a very different thing from saying 
•• man is an animal." 

In view of this fact, Aristotle's four classes of predicables 
may be reduced to two — the first (including definition and 
property) being" convertible, or substitutive; the second 
(including genus and accident) being inconvertible, or attri- 
butive. See Thomson, '- <*>'.». 



44 



OUTLINES OF LOGIC. 



28. What is the distinction between a categorical and 
a conditional judgment ? 

A categorical judgment is one in which some concept, or 
intuition, is directly, and unequivocally, said to belong, or not 
to belong, to some other concept. A conditional judgment is 
one in which the affirmation is made to depend on the truth or 
falsity of some other judgment. To illustrate : the categorical 
judgment says, "A is B" ; or, tc A is not B." The conditional 
judgment says, "If C is D, A is B." 

The term " categorical," as used by Aristotle, has reference 
only to affirmative judgments. His followers- extended the 
significance of the term, so as to cover negatives as well. 



28 : a. State and illustrate Hamilton's Classification 
of Conditionals. 

Hamilton's Classsification of Conditionals is : 



Categorical. 



j Aff 



JUDGMENTS. { 



Conditional. 



I 



Ney. 



"A isB." 
"A is not B." 



Hypothetical (condition in 
subject). " If A is, Bis." 

Disjunct ice (condition in 
predicate) . '*'A is either 
B or C." 

HypotheticO'Disjurn 

(condition in both sub- 
ject and predicate). u If 
A is B, it is either C 
or D." 



Whately makes the terms " conditional" and ", hypo- 
thetical" change places ; and calls the hypothetico-disjunctive 
judgments dilemmatic, trilemmatic, or polylemmatic — accord- 
ing to the number of alternatives which they present. 
Hamilton's nomenclature is decidedly preferable. 



OUTLINES OF LOGIC. 1 .'> 

28 : b. Illustrate the assumed possibility of reducing 
conditionals to the form of categorical s ; 
and indicate what value is to be attached 
to it. 

That conditional judgments can be reduced to the form of 
categorical judgments, is affirmed by Thomson, § 78, and 
Atwater, p. 102 sq., who would, for example, turn the judg- 
ment •• [f A is B, C is I)," into: ;t The case of A's being 1> 
is a case ol' C's being D" ; and the judgment "A is either B, 
C, or D " into: "The possible cases with reference to A are 
B, C and D." 

This reduction is certainly feasible, so far as the form of 
words is concerned — and it may have its advantages in simpli- 
fying the discussion of the process of reasoning ; but it does 
not affect the form of thought — it does not eliminate the 
element of conditionally, but simply expresses it in less usual 
and more barbarous terms. See Hamilton, p. 168 sq. 



29. What do you understand by the distribution c a 
term in Judgment ? 

When the whole of a term, whether that term be subject or 
predicate, is included in any judgment which we form, that 
term is said to be " distributed" ; when the whole of the term 
is not included, it is said to be " undistributed." Thus, 
universal judgments distribute the subject; particular judg- 
ments do not. The expressions " distributed " and "undis- 
tributed" are generally used, however, with reference to the 
predicate onl}' — since the expressions " universal" and 
^particular" serve to denote the distribution or non- 
distribution of the subject. 



29 : n. State and explain the Aristotelian dictum 
concerning the distribution of the predicate. 

Respecting the distribution of the predicate, the Aristotelian 




46 OUTLINES OF LOGIC. 

logicians laid down the dictum that "All negative judgments, 
and no affirmative judgments, distribute the predicate." 

As the Aristotelian logicians never expressed the quantity 
of the predicate in words, some such dictum was necessary in 
order to determine how much of Y was meant when one said 
"X is Y," etc., etc. 

The ground of this dictum with reference to affirmatives 
was, that, judging in the whole of Extension (and to the whole 
of Extension alone the Aristotelian logicians restricted their 
judgments), " X is Y" meant : X is included in 
Y, or is some part of Y. Hence, in an affir- 
mative judgment, like " X is Y," the predicate 
could not be distributed — one could not be 
thinking of the whole of Y. 

With reference to negative judgments, the ground taken 
was, that if we say " No X is Y," yet regard Y as undistri- 
buted, or do not look at the whole of Y, we exclude X from 
that part of Y only which is included in our judgment, and it 
may, for aught we know, be included in that other part of Y 
which our judgment does not contemplate ; in which case it 
would not be true that " No X is Y." To 
illustrate : looking only at the upper part of 
the accompan} T ing diagram, we see no X, and 
form the judgment " No X is Y" ; but some 
one else, looking at the lower part of the 
diagram, detects X, and forms the judgment 
u X is Y," which (viewed from the Aristotelian stand-point) 
contradicts the judgment previously formed. Hence, unless 
in a negative judgment one surveyed the whole predicate, and 
made sure that the subject was excluded from it, he could not, 
according to the Aristotelian logicians, be sure of any valid 
negation. See Thomson, p. 157. 




OUTLINES OF LOGIC. 



47 



29: b. Give the Aristotelian table of judgments as 
determined by this dictum. 

In accordance with the above dictum, the Aristotelian 
logicians— down to, and including Whately — recognized the 
following as the only valid forms of judgment. 

'/"< rms. Quant . 

A. All X is Y. Tniv. 

E. No X is Y. Univ. 

1. Some X is Y. Partic. 

O. Some X is not Y. Partic. 

These different judgments may be illustrated by the following 
jystem of circular diagrams devised by Euler: 



Qual. 


lid. 


A If. 


Attrib 


Neg. 


Subst. 


Aff. 


Attrib 


Neg. 





All X is Y. 



No X is Y. 



I and O. 




Some X is Y. 
Some X is not Y. 



30. Give the table of judgments as recognized by 
Hamilton. 

To the four judgments recognized by Aristotle, Sir William 
Hamilton has added four other judgments, covering all the 
possible combinations of two terms. [2 Terms x 2 Quantities 

x 2 Qualities = 8 forms of judgment.] 



These added Hamiltonian judgments are 

Terms, Quant. 

1. All X is all Y. Univ. 

Y. Some X is all Y. Partic. 

//. Xo X is some Y. I'niv. 

co. Some X is not some Y. Partic. 



Qual. 

Air. 

it 

Neg. 



Bel. 

Subst. 



48 OUTLINES OF LOGIC. 

30 : a. State and illustrate the principle on which 
Hamilton made his additions to the Aris- 
totelian judgments. 

It will be noticed that in all his added judgments Hamilton 
violates the Aristotelian dictum respecting the distribution of 
the predicate ; since both of his affirmative judgments, and 
neither of his negative judgments, include the whole of Y. In 
opposition to this dictum, Hamilton contends that both the 
subject and the predicate of a proposition have a determinate 
quantity in thought (a fact, hy the way, which is seriously 
questioned by some) ; and that this quantity ought, upon 
demand, at least, to be expressed in language. He further 
claims that, when the quantity of the predicate is thus 
definitely expressed, we may have a universal predicate in an 
affirmative judgment, or a particular predicate in a negative 
judgment, just as well as those predicates prescribed by the 
scholastic dictum. 

For example : in the Aristotelian judgment A, we mean to 
affirm that all X is included m, or is a part of, Y. Now, if 
we say what we mean — that is, "All X is some Y" — it leaves 
us free to form the judgment U, "All X is all Y." Similar 
reasoning with reference to I, leaves us free to form the judg- 
ment Y, 6t Some X is all Y." 

Again, in the negative judgment E, we mean to exclude 
the whole of X from any part of Y; and, to express our 
thought fully, should say: "No X is any Y." Then we are 
free to form, if we choose, the judgment ?;, " No X is some 
Y." Likewise, in the negative judgment O, we should say 
what we really mean, " Some X is not any (or is no) Y." 
Then we are at liberty to say, if we see occasion to, " Some 
X is not some Y " — using the judgment go. 

To sum up, in a single sentence, the results of our dis- 
cussion : the principle on which Sir William Hamilton adds 
the judgments U, Y, 7/ and go to the four judgments recog- 
nized by Aristotle, is that of " The Thorough-going 



OUTLINES OF LOGIC. 4 ( J 

Quantification of the Predicate." This is the corner- 
stone of what is called: tk The New Analytic of Logical 
Forms." 

Hamilton's u thorough-going quantification of the predi- 
cate " is. however, facilitated by the interpretation which he 
gives to the copula in a judgment. While the Aristotelian 
reads a judgment only in Extension, and interprets " is" to 
mean " is included in" ; Hamilton reads a judgment either in 
Extension or Intension, and, to cover both, interprets " is" 
to mean : ; - is." Between subject and predicate, according to 
him, the sign of equality may always be placed, and eveiy 
judgment becomes substitutive — a point which will be better 
appreciated when we come to discuss Logical Conversion. 

While, throughout this discussion. I have used the signs 
which Thomson — in common with most logicians — employs to 
designate the Hamiltonian judgments, I prefer the designation 
adopted by the later advocates of the •' New Analytic," 
according to whom the judgments would be classified as 
follows : 





Affirmative. 


Negative. 




Toto-total 
Parti-partial. 
Toto-partial. 
Parti-total. 


AA. All X is all Y. 
II. Some X is some Y. 
AI. All X is some Y. 
IA. Some X is all Y. 


No X is any Y. 
Some X is not some Y. 
No X is some Y. 
Some X is no Y. 


EE. 
00. 
EO. 
OE. 



31. What value is to be attached to the Hamiltonian 
judgments U and Y ? 

The Hamiltonian judgments U and Y have been so gene- 
rally accepted, that Thomson utterly neglects to refer them to 
their author. But while all modern logicians agree in accept- 
ing these judgments, and while there is no question that 
they are actually formed, attention should be called to their 
peculiar character. Possibly, it was from the consideration of 
this peculiarity, and not from mere oversight, that Aristotle 
excluded them from his list. "A judgment," Thomson tells 
an expression that two notions can, or cannot, be 
reconciled" : but, in the judgments D and Y. we do not have 



50 OUTLINES OF LOGIC. 

two notions— we have the same notion expressed in different 
terms. For example: "Sodium Chloride is common salt"; 
"All man is all rational animal."* 

In the last instance, we simply predicate agreement between 
the s}'mbolic and the notative term for the same concept. 
I would not, for this reason, say that U and Y are not valid 
judgments, although even Hamilton's definition of judgment 
does not precisely cover them. The}' are explicative judgments, 
or " semi - identical propositions." See Thomson, § 81; 
Ativater, p. 101. 

To mark a positive increase in our knowledge (or. to mark 
our failure in this direction — which is nearly as instructive as 
success) we must make use of the Aristotelian judgments, 
which refer, or refuse to refer, a class of objects to a higher 
class. These judgments — which may be styled " ampliative," 
in opposition to "explicative" — serve to mark our advances 
in scientific classification. The Hamiltonian judgments U 
and Y — giving us merely equivalent expressions for the same 
notion — serve only to define and clarify knowledge already 
acquired. See the author's Art of Expression, p. 39. 

32. What objections are urged to the Hamiltonian 
judgments Eta and Omega ? 

The judgments 1? and go have been very generally rejected ; 
though Bowen (Logic, p. 132 sq.) strenuously defends them. 
The common, — and, indeed, the valid, — objection to these 
judgments is : that, though they are conceivable, the}' are not 
included in those actual forms of thought with which, alone, 
Logic is concerned. See Thomson, § 79 and note. 

Thomson's objection to ?/, that it " has the semblance only, 
and not the power, of a denial," seems to me not well taken. 
The judgment, "No birds are some animals" (t. e. quadru- 
peds) has the power of a denial. The judgment "All birds 
are some animals" (i. e. bipeds) does not really contravene it ; 



* I find the point here taken (in 18G8) confirmed — even to the first 
illustration — by Bain, Deductive Logic, p. 88, 



OUTLINES OF LOGIC. 51 

nor is it, really. " a judgment of the affirmative kind from the 
Mime terms." The mind is thinking of a different " some" in 
the two judgments. 

To say " No planets are some stars" (//) is, certainly, a 
practicable and efficient denial, if one chooses to employ it; 
but most persons would instinctively prefer the equivalent 

expression: " Some stars are not planets." When we have 
before us two concepts of equal extent — one positive, the 
other negative — we naturally make the positive, rather than 
the negative, the subject of our proposition. 

In defence of the judgment ai, Hamilton argues with great 
ingenuity. See Thomson, p. 164.* His judgment, " Some 



* "To ray objection, that the two weaker negatives have never oc- 
curred in the examination of Logical examples, Sir William Hamilton 
replies, in the AthenGmm (in a letter dated February 25, 1851) as 
follows : * The thorough-going quantification of the predicate (on de- 
mand) in its appliance to negative propositions, is not only allowable, 
is not only systematic, is not only useful, — it is even indispensable. 
For to speak of its very weakest form, that which I call parti-partial 
negation, Some — is not some ; — this (besides its own uses) is the form 
which we naturally employ in dividing a whole of any kind into parts : 
J. is not some A. And is this form — that, too, inconsistently — 
to be excluded from Logic ? — But again (to prove loth the obnoxious 
propositions summarily and at once) — what objection, apart from the 
arbitrary laws of our present Logical system, can be taken to the 
following syllogism ? — 

All man is so?r,e animal, 

Any man is not {no man is) some animal; 

Therefore some animal is not some animal. 

Vary this syllogism of the third figure to any other , it will always be 
legitimate by nature, if illegitimate to unnatural art. Taking it, how- 
ever, as it is — the negative minor premise, with its particular predicate, 
offends Logical prejudice. But it is a proposition irrecusable ; both as 
true in itself, and as even practically necessary. Its converse, again, is 
technically allowed ; and no proposition can be right of which the 
converse is wrong. For to say (^as has been said from Aristotle down- 
wards) that a particular negative proposition is inconvertible, — this is 
merely to confess that the rules of logicians are inadequate to the truth 
of Logic and the realities of nature. But this inadequacy is relieved by 
an unexclusive quantification of the predicate. A toto-partial negative 
cannot, therefore, be refused. — But if the premises are correct, so like- 
wise must be the conclusion. This, however, is the doubly obnoxious 
form of a parti-partial negative : 

>■'! 'man; is not some animal say, brute), 
thing, it may be observed, is more easy than to misapply a form ; 
nothing more easy than to use a weaker, when we are entitled to use a 
stronger proposition. But from the special and factitious absurdity thus 
emerging, to infer the general and natural absurdity of the propositional 
form itself— this is, certainly, not a Logical procedure.'" 



52 OUTLINES OF LOGIC. 

A is not some A" (or, in terms, " Some trees are not some- 
trees") would, however, more naturally be expressed by E 
instead of &? : " No A is any B" ; " No elms are any oaks." 

The conclusion of his syllogism in which he proves both 
the obnoxious propositions summarily and at once, can only 
mean : " Rational animals are not irrational animals" — which 
is grossly tautological. Thomson's objections to go — like his 
objections to ?/ — are not beyond question. " Some X is not 
some Y " may be " true, whatever terms X and Y stand for" 
(Thomson, p. 163) ; but is not true, whatever parts of X and 
Y " some " denotes. " This is not the salt that I bought of 
Jones" evidently denies something ; though it is reducible to 
the obnoxious form " Some is not some " (go). " Some X is 
not some X" would, however, be its fair equivalent rather 
than " Some X is not some Y" — which, in connection with 
Hamilton's " Some A is not some A," where he should have 
given us: "Some A is not some B" (see note, p. 51), 
ma}' suggest that the judgment go is valuable, if at all, in 
discriminating parts of the same concept, rather than parts 
of different concepts. 



32 : a. In what sense does Hamilton use the word 
" some"; and what bearing does this use of 
the word have on these commonly rejected 
judgments ? 

The contemptuous rejection of the Hamiltonian judgments 
generally results from a misconception of the meaning which 
Hamilton attaches to the word " some." This word ma}' 
mean: " Some at least, perhaps all" — in which sense the 
Aristotelian logicians used it; or, it may mean: "Some at 
most, not all." It is in this latter, or semi-definite, sense, 
that Hamilton employs the word "some" in quantification. 
See Logic, p. 531. Thus, when the Aristotelian says : " Some 
X is Y," he means : " Some - possibly, all — X is Y." When 
Hamilton says: "Some X is Y," he means: "Some — 
certainty, not all— X is Y." 

Hamilton's use of the word " some" is, according to Mr. 
Grant White — Words and Their Uses, p. 251 sq, — that which 



OUTLINES OF LOG* . 53 

Etnctioned by the derivation of theword and the usage of 
the best writers. According to White, the word "some" 
denotes u an indeterminate quantity or number, considered 

apart from the whole existing number.' 1 Cf. the author's 
Art . [>. 61. 

Attaching to the word •• some" this semi-definite or Hamil- 
tonian sense. I do not see why we may not form the judgment 
//("NoX is some Y"). If we can say : " Some Y is no X," 
no valid reason can be given why we may not reverse the 
process. See note, p. 51. 

33. Illustrate the assumed possibility of reducing the 
Hamiltonian judgment Y to U. 

It may be remarked, before dismissing the subject under 
discussion, that the judgment Y (" Some X is all Y") is open 
to atill further objection. By •• Some X" Hamilton means to 
indicate an indeterminate part of the wider term X — of which 
indeterminate part, be it more or less, the whole is taken. 
14 Some X is all Y" means, then : 

(All) (Some X) = all Y. 

Now it is claimed that this double predesignation of X is 
still more unnatural in thought than in language—that, 
instead of regarding " Some X " as a part of the wider term 
X. we may. more naturally, regard it as a new term. Let 
me X" = Z. Substituting this expression for ,; Some X," 
the equation 

(All) (Some X) = all Y 
becomes 

All Z = all Y. 

which is the judgment U. 

If this reasoning be accepted (I am indebted for it to one 
of my pupils. Mr. Joseph M. McMaster), we may reduce the 
valid Hamiltonian judgments to one — namely U — which is, 
as we have seen, a semi-identical proposition, or. a definition, 
rather than a judgment. 

I am, however, inclined to question the significance of this 
reduction— regarding the partitive judgment 4 - Some X is 
all Y" as essentiallv different from the non-partitive judgment 
-All Z is all Y." 



54 OUTLINES OF LOGIC. 

34. What do you understand by the Modality of 
Judgments; and what is Aristotle's three-fold division 
under this head? What value is to be attached to this- 
division ? 

By the ** Modality" of judgments, we understand, " the 
degree of certainty with which a judgment is made and main- 
tained." 

Aristotle divides judgments into problematic, which are 
matter of mere opinion (e. g. "It will, probably, rain to- 
morrow") ; assertory, which are sure to him who holds them, 
but not susceptible of demonstration (e. g. "America is, in 
general culture, superior to England") ; and apodeictic, or 
demonstrative, which are not onl} T sure to him who makes 
them, but to all who are of sound mind and able to appreciate 
their statement and defence (e. g. "The sum of the angles 
of a triangle is equal to two right angles"). 

The fact that Thomson, § 118, mades a nine-fold division 
under the head of Modality suggests that no such clear and 
sharp distinction as Aristotle attempts can be maintained. 
" Problematic " judgments shade into " assertoiy " judgments 
by endless variations. Moreover, that which is matter of 
doubt to one person may be matter of assertion to another t 
and matter even of demonstration to a third, (e. g. tl That 
the square described on the hypothenuse of a right-angled 
triangle is equal to the sum of the squares of the two other 
sides"). 

The Aristotelian division is interesting and important as 
underlying the distinction between "moral" and " demon- 
strative " reasoning — or between "proof" and "demonstra- 
tion " — which differ in their sphere, and in the nature of 
their evidence, rather than in their certainty to a reasonable 
being. " Demonstration " consists in tracing a statement back, 
step b}' ytep, till it is seen to rest upon some self-evident 
truth. Its sphere is pure science and, especially, the Mathe- 



OUTLINES OF LOGIC. 55 

maties. " Proof M consists in adducing, in support of a state- 
ment, considerations which may reasonably induce, but do not 
absolutely compel, belief. Its sphere is human knowledge in 
general. "Proof," in its legitimate sphere, may be as con- 
clusive as " demonstration. " You are as certain, doubtless, 
that you exist, as you are that the sum of the angles of a 
triangle is equal to two right-angles. Yet the latter fact is 
susceptible of u demonstration ;" the former, is not. 

Nothing is more stupid than to ask for " demonstration " 
where only " proof" is possible — though this is what religious 
scepticism commonly asks. As Coleridge says (Aids to 
Refection): " The man who will believe nothing but by 
force of demonstrative evidence is not in a state of mind to 
be reasoned with on any subject." 

Dr. Archibald Alexander says: "When all the evidence 
relating to a proposition is before the mind, that is true which 
is easiest to be believed ; because it is easier to believe with 
evidence than against it." To the same effect is Greenleaf 's- 
statement (G-reenlectf on Evidence) that "The subordinate 
rules of evidence are silenced by the most transcendent and 
universal rule that, in all cases, that evidence is good than 
which the nature of the subject presumes no better to be 
attainable." 



34: a. Why is Modality generally referred to Ap- 
plied Logic? 

Whether a judgment be problematic, assertory or demon 
strati ve, its form will be the same. As Hamilton says (Logic, 
p. 183) : " Whatever cannot be stated by A, B and C is not 
of Logical import ; and A, B and C know nothing of the 
necessary, impossible and contingent." The distinctions 
under this head are founded either on the mental culture of 
the individual ; on his opportunities for observation ; or on 
the matter with which he deals. In either case, Modality 
must be excluded from Pure Logic. 



56 OUTLINES OF LOGIC. 

35. Define Reasoning, and distinguish between Imme- 
diate and Mediate Inference. 

Reasoning consists in deriving one judgment from another 
judgment, or other judgments. When we derive one judg- 
ment from another judgment directly and without an\ T inter- 
vening process (as when from the judgment fcC All men are 
mortal," we infer that " Some mortal beings are men "), our 
inference is said to be immediate. When we derive one judg- 
ment from another judgment only by positing a third (as when 
we infer from the judgment " This liquid contains arsenic" 
that "This liquid is poisonous," by laying down the third 
judgment: 4C All liquids containing arsenic are poisonous "), 
our inference is said to be mediate. 



35 : a. Enumerate the various kinds of Immediate 
Inference. 

The various kinds of Immediate Inference are : 

(1) By Opposition. 

(2) By Conversion. 

(3) By Privative Concepts. 

(4) By Added Determinants. 

(5) By Summation of Predicates. 

(6) By Disjunctive Judgments. 

(7) By Interpretation. 

These different kinds of Immediate Inference will be dis- 
cussed in the order in which they are named. 

36. Define Logical Opposition, and give the classifica- 
tion under this head. 

Logical Opposition is that difference existing between two 
judgments which have the same subject and predicate — either 
with reference to quanthrv, qualit} T or relation— by virtue of 
which, when one judgment is affirmed or denied, we are able, 



OUTLINES OF LOGIC. 57 

immediately, to make some inferenoe respecting the truth or 
falsity o( its opposite. 

Under this head the following classification may be accepted : 

True \ 1. Contradictory. No alternative. 
{Quality.) I 2. Contrary. An alternative.; 



OPPOSITION^ False, fl. Subaltern. (Quantity merely. 

(Quantity, [ rt , . ,-,,,. 

v 7 ) 7 . . ' 2. Inconsistent. f Relation merer 
Relation, j 

^S'tme.) ^3. Sab-contrary. Name merely. 



36 : e». Explain the nature of each kind of Opposi- 
tion enumerated in this classification ; the 
judgments between which it exists; and 
the inferences deducible from it. 

try opposition exists between an affirmative and 
a negative judgment which are so related that when we affirm 
one, we must deny at least so much as the other ; and vice 
'. That is, between A and O and between E and I 
according to Aristotle : between E and I only, according to 
Thomson. 

Thomson says: ;; Other writers describe A and O as con- 
tradictories ; but the fact is that we cannot tell from the 
removal of 0, whether we ought to replace it by A or U. Let 
the judgment O ' Some men are not rational animals,' be re- 
moved, 1. e. its truth denied, and that removal will not estab- 
lish A. ; All men are (some) rational animals.' A third 
judgment is possible, namely, that i All men are all rational 
animals ' — the only rational animals there are : and which 
of these two is to apply, cannot be inferred from the O, but 
must be ascertained from the facts in the case." Laws of 
Thought, pp. 178-179. 

Atwater {Logic, p. 112 note,) argues against the rejection 
of the contradictory opposition between A and O : but the 
considerations which he suggests would rather lead us to 
regard the opposition between E and I as " contrary." than to 
regard that between A and O as •• contradictory." It is to be 
remarked that in the case of E and I. we have a " toto-total" 



58 OUTLINES OF LOGIC. 

negative (" None is any* 9 ) opposed to a " parti-partial " 

affirmative ("Some is some.") That is, the two judgments 
E and I are as widely separated as possible, in quantity as 
well as in quality. In the case of A and O, this is not true. 
There, we have a " toto-partial " affirmative (" All is some ") 
opposed to a " parti-total" negative ( t; Some is none") The 
opposition between A and O is, clearly, not so great as 
between E and I. The Hamiltonian U (" All is all") and 
go (" Some is not some") would stand in strictly correspon- 
dent relation to E and I. 

Contrary opposition exists between an affirmative and a 
negative judgment which are so related that from the affirma- 
tion of one we are not compelled to den}' the other, and vice 
versa — that is, where we have an alternative judgment open 
to us, and both the opposing judgments may be false ; though 
the}' cannot, at the same time, both be true. This kind of 
opposition exists, for example, between A andE. That " All 
X is Y " and that " Xo X is Y" cannot both be true ; but the 
truth may be (1) that " Some X is Y " and (O) that " Some 
X is not Y." See Bain, Deductive Logic, p. 92 sq. 

Subaltern opposition exists between two judgments of the 
same quality, of which one ma}' be regarded, by virtue of the 
inferior extension of one or both of its terms, as being 
included in the other. For instance : between A and I. 
The including judgment is called the " subalternant " ; the 
included judgment, the subalternate. To affirm the subaltern- 
ant, affirms the " subalternate." e. g. If " aWX" is included 
in Y. " some X" must be. To deny the subalternate, denies 
the subalternant. e. g. If " some X" is not included in Y, 
Ci all X " cannot be included in Y. But nothing follows from 
denying the subalternant, or affirming the subalternate. 
Though ki all X" is not included in Y, "some X" maybe. 
Though " some X" may be included in Y, ;4 all X " need not 
be. 

Inconsistent opposition exists between two judgments of 
the same quality which cannot both be* true at the same time ; 



OUTLINES OF LOGIC. 



59 



and is especially marked where one judgment is substitutive 
and the other attributive. e. <j. Between A and U. Sec 
Thomson, pp. 179-180. 

Subcontrary opposition, or the opposition which exists be- 
tween two subalternate judgments of different qualit}', is 
merely nominal. Between the Aristotelian I and O (sub-con- 
traries) there is a seeming contradiction, but a possible agree- 
ment. If " some X " be Y, " some X " — that is, some other 
part of X — may, at the same time, not be Y. Reading these 
judgments in the Hamiltonian sense : if it be true that " Some 
X is Y," it must be true that " Some X is not Y." The one 
statement is the necessary complement of the other. 

In regard to the opposition" — called sub-contrary — between 
Y and O, the truth of Y implies the truth of O ; but Y and O 
may both be false — the truth being, for instance, U. See 
Thomson, p. 182. 



37. Give the table which illustrates Logical Opposi- 
tion, embracing the judgments A E I and O. 




60 



OUTLINES OF LOGIC. 



37 : a. Discuss the table from the Aristotelian point 
of view. 

Reading all of these judgments in the Aristotelian sense, 
the effect, on each of the others, of alternately affirming and 
denying A, E, I and 0, is as follows : 

To affirm A, affirms I and denies O and E. 

64 " E, " O " " I and A. 

" " I " E. [possibly O.] 

" " O "A. [possibly I.] 

" deny A " O. [possibly E.] 

" " E " I. [possibly A.] 

" " I denies A, affirms E and 0. 

" " O " E, " A and I. 

Cf. Schuyler, Logic, p. 34. 



37: b. Give tables of Opposition which introduce 
the Hamiltonian judgments. 

If we recognize six forms of judgment only, the following 
table will serve to illustrate Opposition : 




Y^-#"* 



If we recognize all the Hamiltonian judgments, the follow- 
ing table, suggested by one of my students (Mr. Wm, S. 



OUTLINES OF LOGIC. 



Gl 



Sticknev), is the best I have ever seen. Cf. Schuyler, Logic, 
p. 90. 




\Q . 



37 : c. Discuss the table of Hamiltonian Opposition. 

The minute discussion of the table of Opposition from the 
Hamiltonian point of view is comparatively profitless ; since, 
interpreting the copula and the word " some" in the Hamil- 
tonian sense, each judgment becomes simply inconsistent with 
every other. To deny one, affirms something else. To affirm 
one, denies everything else. Still, to attempt the discussion 
affords a very pretty mental gymnastic. 



38. What is meant by Logical Conversion ? Convert 
the judgments A, E, I, O, U, Y. 



Logical Conversion consists in the transposition of the 



<32 OUTLINES OF LOGIC. 

subject and predicate in a proposition. By this process, as 
simplified by modern logicians, 

A, " All X is some Y," becomes Y, " Some Y is all X." 

E, " No X is any Y," becomes E, "NoT is any X." 

I, " Some X is some Y," becomes I, " Some Y is some X. 

O, " Some X is no Y," becomes r/, " No Y is some X." 

U, " All X is all Y," becomes U, " All Y is all X." 

Y, " Some X is all Y," becomes A, " All Y is some X." 

On the significance of immediate inferences of this nature, 
see Thomson, p. 183. 

38 : a. Show how Hamilton has simplified the pro- 
cess of Conversion. 

It will be noticed that, in order simpl}- to convert the 
Aristotelian judgments A and O — as is done above — we are 
obliged to recognize the Hamiltonian judgments Y and t]. It 
is one of the strongest arguments for the acceptance of the 
added Hamiltonian judgments, that onh' b} r accepting them 
can we do away with the cumbrous, unnatural and inadequate 
system of conversion imposed by the Aristotelian dictum. — 
See note, p. 51. 

33: b. Explain the three kinds of Conversion re- 
cognized by the old logicians. 

The old logicians recognized three kinds of Conversion. 

(1) Simple, which, as has already been explained, consisted 
in the mere transposition of terms ; but which the}' employed 
only in the case of E and I. 

(2) By Limitation (conversio per occidens), which was 
employed in the case of the judgment A, where " simple 
conversion" — yielding the judgment Y — would violate the 
Aristotelian dictum respecting the distribution of the predi- 
cate. To avoid this result, the predicate was changed in the 
conversa from universal to particular. Thus A, "All men are 
[some] mortals," was converted into I, "Some mortals are 
[some] men." This method of conversion is obviously de- 
fective, in that we cannot, by re-conversion, regain the 
original judgment. 



OUTLINES OF LOGIC. G3 

(3) By Contraposition^ which was employed in the case of 
the judgment O, which, simply converted, would yield 7/, and 
so violate the Aristotelian dictum ; and which could not be 
converted by limitation without distributing a term in the 
conversa which is not distributed in the convertend. Take, for 
example, a judgment in terms: u Some quadrupeds are not 
[any] horses." This judgment, converted simply, would 
yield // : w * No horses are some quadrupeds" — violating the 
dictum. Converted by limitation, it would yield: t; Some 
horses are not quadrupeds" — i. e. "not any quadrupeds" — 
distributing a term in the conversa which was not distributed 
in the convertend, and involving manifest absurdity. Hence 
the method of * k conversion by contraposition" was devised, 
which consists in transferring the negation from the copula to 
the predicate, and thus transforming the judgment O to a 
judgment I, which could be simply converted. Thus, instead 
of O, tfc Some quadrupeds are-not horses" (non sunt equi), we 
have I, " Some quadrupeds are not-horses" (sunt non-equi), 
which could be converted, without violating the dictum, 
into: " Some not-horses are quadrupeds." See Ativater, pp. 
113-117. 



39. Explain and illustrate what is meant by Immediate 
Inference by Privative Concepts. 

" Positive" concepts, as we have already seen (p. 34), imply 
corresponding " privatives." Every judgment concerning 
positive concepts, consequently, implies judgments respecting 
their corresponding privatives. u Immediate Inference by 
Privative Concepts" consists in drawing out, and stating, these 
implied judgments. For instance, the judgment "All men 
are mortal' 1 (positive) implies the judgment, that " No men 
are immortal" (privative). Great care is necessary in draw- 
ing these inferences — especially not to distribute a term in the 
inferred privative which was not distributed in the positive 
from which the inference was drawn. 

As is done by Thomson in the second privative assigned to 
his first positive on page 186. 

These inferences are useful not only because we frequently 



64 OUTLINES OF LOGIC. 

throw a judgment into one of these inferential forms before 
determining upon its reception or rejection ; but because it is 
frequently easier to maintain a negative than a positive propo- 
sition. It is to be noticed that two privatives, instead of one, 
may be introduced into the inferred judgment ; and that 
"Immediate Inference by Privative Concepts" is frequently 
complicated by "Conversion." Thus from U A11 men are 
mortal" we infer that "Any immortal beings are not-men" 
See Thomson, who emphasizes the importance of this subject, 
§ 86. 

40. Explain and illustrate what is meant by Immediate 
Inference by Added Determinants— by Composition of 
Judgments. 

"Immediate Inference by Added Determinants" depends 

upon the principle that " if equals be added to equals, their 

sums will be equal." e. g. 

a = b 
c = c 



.-. ac = be ; 
or, in terms, (see Thomson, § 87) : "A negro is a fellow- 
creature"; therefore: "A suffering negro is a suffering 
fellow-creature." Here, the subject and the predicate of a 
judgment have simply been made more " determinate," by the 
addition to each of the same mark. The mark added must 
not be incompatible with the objects to which it is added. 
For example : "A sky-blue negro is a sky-blue fellow-creature'* 
would be sheer nonsense ; yet, here we have added equals to 
equals. 

By a still further application of the principle already stated 
and illustrated, we may have what might well be called 
Immediate Inference by Composition of Judgments, for which 

the formula would be : 

a = b 
c = d 

. • . ac = bd ; 



OUTLINES OF LOGIC. 65 

or, in terms, ki Honesty deserves reward," and " A negro is a 
fellow-creature"; therefore: " An honest negro is a fellow- 
creature deserving reward." Care must here, also, be taken 
that the judgments compounded are not incompatible with 
each other. 

41. Explain and illustrate what is meant by Immediate 
Inference from the Summation of Predicates. 

On the principle just explained and illustrated, we may also 
add together several judgments which have the same subject 
but different predicates. It is by thus combining several 
judgments A that we get a definition, or a judgment U ; since r 
though a given object may share any one attribute with many 
other objects, each attribute ascribed to it eliminates some of 
those objects until, by the summation of a sufficient number of 
predicates, we get a result which is proprius to the object 
under discussion, and may serve as a definition. 

84 The definition of copper, for example, that it is l a metal 
— of a red color — and disagreeable smell — and taste — all the 
preparations of which are poisonous — which is highly 
malleable — ductile — and tenacious — with a specific gravity of 
about 8.39/ is the result of as man} 7 different prior judgments 
as there are properties assigned." Thomson, p. 191. 

Other bodies ma}' share each of these properties with 
Copper ; but no other body possesses them in combination. 



42. Explain and illustrate the immediate inferences 
which are possible from a disjunctive judgment. 

Thomson, § 90, gives two formulas to illustrate this kind of 
Immediate Inference : 

(1) All A is x, y or z. Therefore (on the principle that 
the dividing members must mutually exclude each other), the 
x of A is not the y or z of A. 

(2) All A is x, y or z. Therefore (on the principle that 



G6 OUTLINES OF LOGIC. 

the dividing members must completely exhaust the divisum) y 
the not-x of A is the y or z of A. 

For an illustration in terms : "All teeth are either incisors, 
canine, bicuspid or molar." Formula 1 : "A canine tooth is 
not a molar tooth"; Formula 2 : "A tooth not canine must 
be incisor, bicuspid or molar." 

Great care is necessary, with reference to this important 
class of immediate inferences, that all the dividing members- 
be enumerated, and that they absolutel} T exclude each other. 
" Imperfect Disjunction" is one of the most fruitful sources of 
fallacious reasoning. 

43. Explain and illustrate what is meant by Imme- 
diate Inference from Interpretation. 

It has already been seen that every judgment may be read, 
or interpreted, in the three wholes of Extension, Intension 
and Denomination. These different readings afford, according 
to some, so many " inferences from interpretation." The term 
may better be applied, however (see Thomson, § 89), where 
we infer from such a judgment as "A is B" that such a thing 
as B actually exists. This form of immediate inference is, 
unquestionably, of practical value. To illustrate by an 
actual example of its use: "You cannot doubt that Dea. S. 
is a real Christian." " O ! no, I concede that." "Then, 
you must concede that such a thing as Christianity really 
exists." 

44. Illustrate the importance of Ilmmediate Inference, 
by showing how much is involved in the judgment : 
" All men are mortal." 

The Importance of Immediate Inference is so generally 
underrated, that we introduce the illustration suggested, but 
not very clearly stated, by Thomson, § 92. The judgment 
"All men are mortal" means : 



OUTLINES OF LOGIC. G7 

Head in E Man is one species in the class of 

mortal beings. 

Read in Tnti rmon, The attribute of mortality should always 

accompany our notion of man. 

Bead in Denomination, The word " mortal" ma}' always be 
applied to man. 

By Subaltern Opposition, Any given man is a mortal. 

By Contradictory Opposition, It is false that u Some men 
are not mortals." 

By Contrary Opposition, It is false that u No men are 
mortals." 

By Inconsistent Opposition, It is not true that men are all 
the mortal beings. 

By Aristotelian Conversion, It is true that some mortals are 
men. 

By Hamiltonian Conversion, It is true that some mortals are 
all men. 

By Privative Concepts, Xo men are immortal. 
" " " Any immortal beings are not men. 

By Interpretation, There is such a thing as mortality. 

By Added Determinants, A man with immortal hopes, is a 
mortal with immortal hopes ; 

He who honors a man. honors a mortal. 

By Composition of Judgments, Since heaven is immortality, 
a man expecting heaven is a mortal expecting immortality. 



45. Define the Syllogism ; and explain how it origin- 
ates, and what its essential parts are. 

The syllogism (Gvv-\oy[£eiv) may be defined as the 
formal statement of the process by which we derive one judg- 
ment from another through the medium of a third. 

In discussing the syllogism, it is best to view it with refer- 
ence to its origin and development, which may be traced aa 
follows : 



68 OUTLINES OF LOGIC. 

(1) A question arises which of two contradictory predicates 
is to be affirmed of a given subject, e. g. " Is this disease 
fatal or not-fatal"— " Is X, Y or not-Y" ? Of course, it must, 
on the principle of kt excluded middle," be one or the other. 

(2) This question leads to the affirmation of some general 
principle by means of which we hope to arrive at a solution of 
our problem, e. g. "All consumptions are fatal" — " All Z 
is Y." 

(3) The next step is to apply the general principle, if pos- 
sible, to the case in hand. On examination, we are enabled to 
affirm, for example : " This disease is a consumption" — " X 
is Z." 

(4) Then, what was at first proposed as an alternative pre- 
dicate, follows as a conclusion. For example : " Therefore 
this disease is fatal "— " X is Y." 



45 : a. What is meant by " subject" and " predicate," 
"middle," "major" and "minor" terms; 
and what objection may be made to the 
latter nomenclature? 

It will be seen that, in every syllogism, three terms are in- 
troduced. Of these, the one which appears as subject of the 
conclusion (and which was, also, the subject of the problem- 
atic statement originally proposed for solution) is called, 
throughout the syllogism, the subject and designated by the 
letter S. The predicate of the conclusion (which was the 
alternative predicate in the original problem) is called, 
wherever it may stand in the syllogism, the predicate and des- 
ignated by P. The term with which both the subject and 
predicate are compared is called the middle term and desig- 
nated by M. 

To illustrate, we ma} T express the syllogism just given, in 
symbols as follows : 



OUTLINES OF LOGIC. 



&.> 



All consumptions are fatal, MP, 

This disease is a consumption, SM, 
Therefore, this disease is fatal, SP. 

The subject was formerly called "the minor term," and the 
predicate "the major term;" because, 
reasoning — as the Aristotelians did — in 
the whole of Extension, the predicate 
was major, greater ; the subject, minor, 
less, than the middle term. e. g. 31 is 
included in P. S is included in M. .-. S 
is included in P. 

If, however, we argue in the whole of Intension, we get 
an equally valid conclusion ; yet the expressions major and 
minor term should change places, e. g. m comprehends p, 
s comprehends m, .-. s comprehends p. 

If we recognize the validity of substitutive judgments, and 
understand the copula to mean " is equivalent to," we get an 
equally valid conclusion ; yet the distinction of the subject 
and predicate terms, so far as magnitude is concerned, van- 
ishes altogether, e. g. 






On this subject, Thomson (p. 194) makes some remarks- 
which do not, to my mind, show the absurdity of the old 
nomenclature so decidedly as he thinks. His objection over- 
looks the fact that Pure Logic has to do with " formal " not 
"material" Extension. For instance: in the judgment 
" Some brave men are prudent," it is not necessary to deter- 
mine how many men are covered by the terms i; brave " and 
••prudent"; but merely whether the latter class, taken as a 
whole, includes an}- of the former. I agree with Thomson, 
however, in wishing the old nomenclature banished ; and wish, 
further, that the new nomenclature did not involve the absurd- 
ity of calling a term "the subject" when it is, really, a 



70 OUTLINES OF LOGIC. 

predicate; and " the predicate," when it is, really, a sul> 
ject. e. g. 

MP, PM, 

Third Figure. MS, Second Figure. SM, 

S P. S P. 



45: b. What are the premisses? Do they always 
precede the conclusion in expression— in 
thought? 

By the ' ' premisses " {pre and mittere) we mean the two 
judgments from which the conclusion is derived and which, in 
the formal statement of the syllogism, ordinarily precede the 
conclusion. They do not, however, necessarily precede the 
conclusion either in expression or in thought. Frequently, we 
state our conclusion first, and then give the reasons by which 
we support it. Not infrequently, we form our conclusion upon 
vague and general considerations and subsequently devise 
arguments in its defence. See Thomson, § 94. 

45 : c What is meant by the "major" and the "minor" 
premiss? What objection to this nomen- 
clature? What does Hamilton propose to 
substitute ? 

The general principle referred to in our analysis of the s} r l- 
logism is commonly called " the major premiss"; the refer- 
ence of the case in question to the general principle is com- 
monly called u the minor premiss" — since in the first, the 
"major," in the second, the " minor" term is compared with 
the middle term. But, if we reject the names "major" and 
" minor "term, we ought not to retain the names, " major" and 
u minor" premiss. Further : the " premisses " are, as we have 
seen, not alwa} T s, either in expression or thought, sent before 
the conclusion. In view of these facts, Hamilton proposes to 
call the affirmation of the general principle (or "the major pre- 
miss ") the sumption; and the reference of the particular case 



OUTLINES OF LOGH , 71 

to the general principle (or "the minor premiss") the sub* 
prion. The change which he proposes is desirable; but 
the old nomenclature has so thoroughly passed into literature 
that it is hardly possible to supplant it. 

45 : (I. What does Thomson propose to substitute 
for "major" and "minor" premiss ; and what 
objection is there to his nomenclature? 

Thomson proposes to call ; * the major premiss," the first 
premiss: and •• the minor premiss," the second premiss. 
JPredicate-premiss and subject-premiss would introduce greater 
harmony into his nomenclature ; and would be preferable from 
the fact that, in an analytic syllogism (or one in which the 
conclusion is given first, while the premisses follow as reasons 
for its adoption), his wi second premiss" would stand firsts and 
his " first premiss," second. See Thomson, p. 200. 

Unless we accept the decided innovation which Hamilton 
proposes, we had better continue to say " major premiss " and 
11 minor premiss." There is, indeed, a sort of fitness in this 
nomenclature ; since the major premiss is broader and more 
general than the minor. 

46. Enumerate and explain the commonly accepted 
rules for the conduct of the Syllogism. 

(1) There must, in a syllogism, be three terms and only 
three. 

(2) There must, in a syllogism, be three judgments and 
only three. 

We are endeavoring to determine the agreement, or non- 
agreement, of a subject and predicate by comparing them with 
an intermediate term. Hence three terms only ; and three 
judgments only — one to compare the predicate with the mid- 
dle term, one to compare the subject with the middle term. 
one to express the result of this two-fold comparison. 

(3) There must be at least one affirmative premiss. 

(«) If neither premiss is affirmative, we have no conclu- 
sion. If M has nothing to do with P, and S has nothing to 



72 



OUTLINES OF LOGIC. 



<lo with M, we have, manifest^, no ground for a conclusion, 
•cither affirmative or negative, respecting the relation of S 
to P. 

(b) If both the premisses are affirmative, we have an affirm- 
ative conclusion. 

(c) If either one of the premisses is negative, we have a 
negative conclusion. Whether we refuse to posit the general 
principle (*. e. negative the major premiss) ; or refuse to refer 
the particular case to the general principle (i. e. negative the 
minor premiss) we have equally a negative conclusion. 
Either of the following syllogisms, for example, is equally 
valid and conclusive : 



Major Premiss denied. 



No M is P. 

All S is M. 
No S is P. 





Minor Premiss denied. 





All M is P. 

No S is M. 
No S is P. 



Reasoning according to Aristotle, a negative minor premiss 
is impossible in the first and third figures — terms which will 
be immediatel}' explained — for reasons that will, hereafter, 
be given (Topic 50). In the second figure (PM, SM, S P,) 
a valid negative conclusion follows— strictly according to 
Aristotle — from either a universal or a particular negative 
minor premiss, e. g. 



2. Fig. 

Mood, 

Camestres. 

2. Fig. 

Mood, 

Bar oho. 



All men are rational. 
No frogs are rational. 
No frogs are men. 

All horned cattle are ruminants. 
Some beasts are not ruminants. 
Some beasts are not horned cattle. 



OlTl.INl- <»l LOGIC. 



<o 



(4) The "worst relation n established between the middle 
term and either of the other terms, in the premisses, must be 
expressed in the conclusion. See yVto?)iso><, p. 195. 

The word M relation " is used here in the technical sense 
already indicated. See Topic 20 : and cf. Thomson, £ 6§. 
The best relation possible between two terms is that of com- 
plete equivalence — "All is all"; the next best relation is, 
11 All is some " ; the worst is, " Some is some." 

With these explanations, the following syllogism and dia- 
gram will illustrate the application of the rule just given. 



All M = All P. . 



0-O 



All S = Some M. 






All S = Some P. 



(5) Both the subject and the predicate must be compared 
with the same middle term. 

(a) This is ordinarily secured by " distributing" the middle 
term in one of the premisses (as in the syllogism just given) ; 
tor. manifestly, if either of the terms of the conclusion be 
compared with the ichole of the middle term, and the other 
term of the conclusion be compared with any part of the 
middle term, the two terms of the conclusion will be com- 
pared with the same thing. 

If the whole of the middle term be not introduced into one 



74 OUTLINES OF LOGIC. 

of the premisses, then, one of the following conditions must 
be fulfilled. 

(b) The part of the middle term with which the two other 
terms are compared, must be distinctly specified to -be the 
same. e. g. 

Some M is P, 

S is the same M, 
.-. Sis P. 

(c) In the two premisses combined, the middle term must 
be distributed and something more — that is, more than the 
whole of the middle term must be clearly introduced. This 
somewhat irregular method of securing a comparison of the 
subject and predicate with the middle term is illustrated by 
Thomson (p. 198) in the following syllogism and diagram : 

Three-fourths of the army were Prussians ; 
Three-fourths of the army were slaughtered ; 
Therefore, some who were slaughtered were Prussians. 



Prussians : 
Army : j_ 

Men slaughtered : 



Hamilton (Logic, p. 586 sq.) claims that the case (c 1 ) 
which, in this form, is certainty exceptional and foreign to 
pure Logic, really covers all cases. In («), beyond all ques- 
tion, we introduce in the two premisses combined, the middle 
term and something more ; and (b) — like (c), in the form just 
given — is, clearly, foreign to pure Logic. 

A violation of the rule that we have just been discussing, 
involves the fallacy of 4w undistributed middle." 

e. g. Some M is P, 
S is some M, 
.•• Nothing, for there is no certainty that S and P are 



OUTLINES OF LOGIC. 75 

compared with the same part of M. The following diagram 
illustrates this fallacy : 




(6) Neither term of the conclusion must be distributed, 
unless it is distributed in the premiss. The violation of this 
principle is called " illicit process." e. g. 

All consumptions are \_some] fatal. 
This disease is not a consumption. 
.-. It is not [any'] fatal. 

47. What is meant by the Figure of a Syllogism ; and 
what "figures" have been recognized by logicians? 

By the i; figure" of a syllogism, we mean the position of 
the middle term, with reference to the subject and predicate 
terms, in the premisses. See Thomson, § 95. 

Four arrangements of the terms in the premisses of a syllo- 
gism are possible; and four u figures " have, consequently, 
been recognized by logicians. 

1. 2. 3. 4. 

M. P, P. M, M. P, P. M, 

S. M, S. M, M. S, M. S, 

S. P. S. P. S. P. S. P. 



47 : a. Which of the figures affords the most nat- 
ural arrangement of terms? 

It has been claimed (and, I think, with justice) that the first 
figure is more natural than either of the others ; because, in 
that figure, the terms which appear as subject and predicate in 
the conclusion, stand as subject and predicate in the premisses. 

Thomson, however, claims that (since the more extended of 



76 OUTLINES OF LOGIC. 

two terms naturally stands as the predicate of a proposition) 
if we recognize the middle term as more extended than the 
Other two, the second figure, in which the middle term is the 
predicate of both premisses, is more natural than the first ; 
while, if the middle term is, obviously, less extended than 
the other two, the third figure — in which it stands twice as 
subject — is most natural. See Laws of Thought, pp. 201- 
205. It is to be remarked, in this connection, that to deter- 
mine the comparative extent of the terms introduced in a 
syllogism would take us be}~ond the sphere of Pure Logic. 

The third figure is certainly more natural than either of the 
others for inductive reasoning; since the inductive syllogism 
falls, regularly, into the following form : 

X, Y, Z are ruminants, MP, 
X, Y, Z are all horned cattle, MS, 
.*. All horned cattle are ruminants, SP. 



47 : b. What objections have been urged to the 
fourth figure ? 

The unnaturalness of the fourth figure, — in that the terms 
which appear in the conclusion as subject and predicate have, 
neither of them, appeared in the premisses in that capacity, — 
is obvious. It is further urged against the fourth figure that 
it is " a mere perversion of the first figure, in which the proper 
conclusion does not appear, but the converse of it gained by 
Immediate Inference." See Thomson, p. 207. Hamilton's 
objection {Logic, p. 302 sq.) is even more weighty. He 
characterizes the fourth figure as "A monster, undeserving of 
toleration — a hybrid, unnatural, useless and Logically invalid ; 
the premisses being in the whole of 
Extension, and the conclusion in the 
whole of Intension. P is included in M ; 
M is included in S ; therefore, S is in- 
cluded in P? Xo, for S is the greatest 
whole and P. the smallest part ; but S 
comprehends P." 

It is noteworthy that the fourth figure 
was not recognized by the early disciples 
of Aristotle ; but is a comparatively recent addition to 
Logical science. 







OUTLINES OF LOGIC. 77 

47 : c What importance is now attached to Logical 
Figure ; and how is it possible to do 
away with Figure altogether P 

Great attention was paid to Logical Figure by the Aristo- 
telian Logicians down to, and including, Whately ; because, 
accepting the Aristotelian dictum with reference to the distri- 
bution of the predicate, the question whether a term appeared 
in the premisses as subject or predicate was a matter of prime 
importance, and might affect the whole process of reasoning. 
If, with most modern logicians, we reject the Aristotelian 
dictum, and accept Hamilton's explicit quantification of the 
predicate, the significance and value of Logical Figure utterly 
disappears ; and the Science of Thought is thus conformed to 
the thinking processes of the unlettered masses ; who, if they 
can only establish a tangible connection between two terms? 
never stop to inquire which term is subject and which is 
predicate. 

Not only is Logical Figure, by recent modifications of 
Logic, rendered insignificant; but Logical - Figure may, by 
44 the unfigured syllogism" — suggested by Sir William Hamil- 
ton — be done away with altogether. For example, in the 
syllogism : 

Copperas and Sulphate of Iron are identical ; 

Sulphate of Iron and Sulphate of Copper are not identical ; 
.-.Copperas and Sulphate of Copper are not identical, 

w r e get a perfectly valid conclusion ; though Logical Figure 
has entirely disappeared. See Hamilton, p. 587 ; Thomson, 
§ 98 ; Atwater, pp. 142-143 ; The Port Royal Logic, chap. 10 ; 
and Jevons, Principles of Science. 

48. How have the Fundamental Laws of Thought 
been stated in their application to syllogistic reasoning ? 

The Aristotelian stated these laws in the "dictum de omni 
et nullo" — namely: "Quicquid de muni valet, valet, etiam 



io OUTLINES OF LOGIC. 

de qiribusclam et singulis." For other statements of this 
dictum, see Thomson, g 95 and notes. 

This dictum is applicable only to syllogisms in the first 
figure, to which the Aristotelian reduced syllogisms in either 
of the other figures before testing them by the laws of the 
s}'llogism. Separate dicta have, however, been supplied for 
each of the other figures (for which, see Thomson, id supra) ; 
but, with the neglect of " figure," these dicta have fallen into 
comparative insignificance. Hamilton (Logic, p. 559 sq.) 
gives an exhaustive discussion of the entire subject. 



49. What is meant by the Mood of a syllogism ? 

The " Mood" of a s}'llogism expresses the character — with 
reference to Quantity, Quality and Eelation — of the three 
judgments which compose it. Thus, we have the mood AAA, 
indicating a syllogism made up of three judgments, each of 
which is universal, affirmative and attributive. See Thomson, 
§ 99. The syllogism that we gave in our primary analysis 
of " mediate inference" is an example of the mood AAA. 

" Logical Mood" was, formerly, like " Logical Figure" 
(and for similar reasons), regarded as of prime importance. 
It has (for similar reasons) fallen into comparative neglect. 



49 : a. How many moods are possible, and how 
many valid, according to Aristotle— Ham- 
ilton— Thomson ? 

The possible moods will be all the conceivable combinations,, 
in groups of three, of the judgments recognized. That is : 

According to Aristotle, 4x4x4= 64 possible ; 10 valid. 
" " Hamilton, 8 x 8 x 8 — 512 " 108 " 

" " Thomson, 6 * 6 x 6 = 216 " 62 " 

For a table of the valid moods (recognizing D and Y) , see 
Thomson, Laivs of Thought, p. 210. 



OUTLINES <>F LOGIC. 79 

49 : (>. Why are not all the possible moods valid? 

Because many of them violate the rules for the conduct of 
the syllogism. Thus EEE would draw a conclusion from two 
negative premisses; AAE, a negative conclusion from two 
affirmative premisses ; EAA, an affirmative conclusion from a 
negative major premiss; AIA does not follow the "worst 
relation" ; AEO involves " illicit process" [All M is some P ; 
No S is any M ; Some S is no P] ; III involves "undis- 
tributed middle," etc., etc. 



50. Give and explain the mnemonic lines which indi- 
cate the valid moods in the four figures, with the method 
of converting the other figures to the first. 

The mnemonic lines (which were of prime importance to 
the Aristotelian logician) are : 

BArbArA, CElArEnt, DArll, FErlOque, pnom; 
CEsArE, CAmEstrEs, FEstlnO, BArOkO (or FAkOrO), 

secundae ; 
Tertia DArAptI, DIsAmls, DAtlsI, FElAptOn, BOkArdO 

(or DOkAmO), FErlsO habet ; 
Quarta insuper addit: BrAmAntlp, CAmEnEs, DImArIs r 

FEsApO, FrEsIsOn. 

These lines are designed to indicate the valid moods in each 
figure ; and embody rules for the reduction of syllogisms in 
the second, third and fourth figures to the first figure, in order 
that they may be tested by the dictum de omni et nidlo. Since 
the introduction of separate dicta for the second and third 
figures, the mnemonic lines have lost their practical value. 

It may be noted, however, that the vowels which enter into 
the words in the first line, indicate the valid moods in the first 
figure, etc., etc. 

The consonants with which the words in the last three lines 
begin, indicate the mood of the first figure to which the moods 
of the second, third and fourth figures are to be reduced. For 
instance : Cesare, Camestres and Camenes are to be reduced 
to Celarent, which begins with the same consonant. 

S, following a vowel, indicates that the judgment w r hich 
that vowel denotes, is to be converted simply for purposes of 
reduction ; p, that it is to be converted per accidens; k, that 
it is to be converted by contraposition. M (mutanda) indi- 



80 OUTLINES OF LOGIC. 

cates that, in reduction, the premisses are to be transposed. 
The other letters are of no especial significance, being used 
only to make up words. 

Take, for illustration, the following 3yllogism given in the 
Third Figure, Mood Darapti : 

All Z is Y, MP, 

All Z is X, MS, 

.*. Some X is Y, S P. 

This S}'llogism must be reduced to Darii in the First Figure. 
All that is necessary is to convert the minor premiss per acci- 
dens and we have : 

All Z is Y, MP, 
Some X is Z, SM, 
Some X is Y, S P. 

For further illustrations of this reduction, see Schuyler, 
Logic, p. 73. 

It should be observed that not all the moods which are valid 
according to the Aristotelian dictum, are valid in every figure. 
Thus, in the first figure, the minor premiss must be always 
affirmative and the major premiss always universal. If the 
major premiss be negative, the minor premiss must be affirma- 
tive to avoid " negative premisses." If the major premiss be 
affirmative, the major term, standing in the predicate, must be 
particular ; and to have a negative minor premiss would give 
a negative conclusion, distributing the major term and involv- 
ing t; illicit process." Hence, the minor premiss must, in the 
first figure, be affirmative. But an affirmative minor premiss 
cannot distribute the middle term. Hence, to distribute the 
middle term, the major premiss must be universal. 

Again, the second figure can yield only negative conclu- 
sions ; because the middle term, being a predicate in both 
premisses, requires a negative premiss (w T hich involves, of 
course, a negative conclusion) to distribute it. 

Again, the third figure yields only particular conclusions. 
In this figure, both the major and the minor terms, standing 
as predicates in the premisses, can only be distributed by ne- 
gation. If both premisses be negative, we have, of course, 
no conclusion. If the minor premiss be negative (to secure a 
universal - conclusion by distributing the minor, or subject 
term) we shall have " illicit process " ; for the negative con- 
clusion involved by a negative minor premiss would distribute 



OUTLINES OF LOGIC. 81 

the major, or predicate, term which was undistributed in the 
premisses. It being, thus, impossible, in this figure, to dis- 
tribute the subject term, we must have a particular conclusion. 

It will be seen that the restrictions upon these figures is 
founded wholly upon the Aristotelian dictum with reference to 
the distribution of the predicate — with the rejection of which 
dictum the restrictions vanish, and •* figure" itself becomes so 
insignificant as hardly to deserve mention. 

The mnemonic lines are given, partly as a curious bit of 
Logical history, and partly to illustrate the value of Sir 
Win. Hamilton's contributions to Logical Science. 



51. Explain the nature of the Conditional Syllogism, 
and classify syllogisms of this nature. 

In the Conditional Syllogism, the major premiss at least — 
sometimes, also, the minor premiss — is a conditional judg- 
ment. Conditional syllogisms are classified, according to the 
nature of the major premiss (see Topic 28 : a) , as Hypothetical, 
Disjunctive and Hypothetico-Disjunctive. 



51 : a. State and illustrate the laws which govern 
the Hypothetical Syllogism. 

The Hypothetical Syllogism is founded on the principle of 
i; reason and consequent" (see Topic 10), and governed by 
the following laws : 

(1) If the antecedent be affirmed in the minor premiss, the 
consequent must be affirmed in the conclusion, e. g. 

If A is B, CisD. 

A is B, 
.-. C isD. 

(2) If the consequent be denied, the antecedent must be 
denied, e. g. 

If A is B, C is D. 

C is not D, 
.-. A is not B. 



82 OUTLINES OF LOGIC. 

(3) If the antecedent be denied, no conclusion follows ; for 
the consequent may be true on other grounds, e. g. 

If A. B. C. be a corrupt man, he is unfit for office ; 
He is not a corrupt man ; 
.•.Nothing — for A. B. C. may not know how to read or write. 

To draw a conclusion here, would involve " illicit process. " 
We should infer from A. B. C.'s not being some unfit for office 
that he is not any unfit for office, e. g. 

All corrupt men are unfit for office [some] ; 
A. B. C. is not a corrupt man ; 
.•.He is not unfit for office [any]. 

This fallacy is very common, and very deceptive. We need 
to remember, that to deny the antecedent of a hypothetical 
yields no valid conclusion, unless the relation betiveen the ante- 
cedent and the consequent is uniform and invariable — as, for 
instance, in the judgment : " If the thermometer indicates less 
than 32°, ice is formed." 

(4) If the consequent be affirmed, no conclusion follows ; 
for the consequent may be affirmed on other grounds than 
those laid down in the antecedent, e. g. 

If a community is intelligent, it will establish schools ; 
This community establishes schools ; 
.-.Nothing — for it may establish schools under compulsion, 
or from a spirit of rivalry. 

To infer the intelligence of the community from the fact 
that it establishes schools, would involve the fallacy of 
" undistributed middle" (see p. 75). e.g. 

All intelligent people are some people establishing schools ; 
These people are some people establishing schools. 
.-.Nothing. 

Here, as in the previous case, no inference is possible unless 
antecedent and consequent are inseparably connected ; yet 






OUTLINES OF LOGIC. 83 



many editors are no wiser than a little boy of my acquaint- 
ance, who having heard it maintained that there would be a 
panic if Greeley were elected, inferred, from the financial 
stringency which followed the presidential campaign, the 
election of Greele^y. 

The illustration just given suggests the necessity of scruti- 
nizing the major premiss in syllogisms of this nature, with 
especial care ; since it frequently embodies matter of opinion 
rather than matter of fact. 



51 : h. Explain and illustrate the Disjunctive 
Syllogism. 

Attention has already been called (see Topic 42) to the 
" immediate" inferences which are possible from a disjunctive 
judgment. The disjunctive judgment also yields some 
simple " mediate" inferences which ought to be, at least, 
enumerated. 

If either term of a disjunctive judgment be affirmed of some 
new term, the other term of the disjunctive judgment may be 
affirmed of the new term. e. g. 

A is either x, v or z. 
B is A. 
.\ B is either x, y or z ; 
B is either x, y or z, 
.-. B is A: 

B is x [or B is v ; or B is z], 
.-. B is A. 
If either term of the disjunctive judgment be denied, as a 
whole, of a new term ; the other term of the disjunctive judg- 
ment may be denied, as a whole, of that new term. e. g. 
B is not A, 
.-. B is neither x, y nor z : 
B is neither x, y nor z, 
. • . B is not A. 
But nothing follows from denying the predicate of a dis- 
junctive judgment, in part, of a new term. e. g. 
A is either x, y or z, 
B is not x, 
.*. Nothing— it may be either y or z. 

The principles on which these mediate influences rest, have, 
already, been sufficiently explained (see Topics 21 and 42). 



34 OUTLINES OF LOGIC. 

51: e. Classify and illustrate the Hypothetico-Dis- 
junetive Syllogism. 

Of the Hypothetico-Disjunctive Syllogism, there are three 
forms, which are classified according to the character of the 
major premiss. Thus we may have, in the major premiss : 

(1) A common antecedent and a plurality of consequents — 
If A is B, either C is D or E is F. 

(2) A plurality of antecedents and a common consequent — 
If A is B or C is D, then E is F. 

(3) A plurality of antecedents and a plurality of conse- 
quents—If A is B, C is D ; and if E is F, G is H. 

All the forms of the Hypothetico-Disjunctive Syllogism are 
governed by substantially the same rules as the Hypothetical 
S} r llogism ; though those rules are complicated by the fact 
that in some cases the antecedent — in others, the consequent 
— may be affirmed or denied in part rather than as a whole. 
See Ativater, pp. 158-151. 

The following examples in terms will, probably, serve bet- 
ter than any formal statement, to explain the application of 
these rules : 

Class 1. (Common antecedent and plurality of conse- 
quents) : 

If A. B. is a demagogue, he will either rule or ruin. 
fc He is a demagogue {antecedent affirmed); 

.*. He will either rule or ruin. 

He will neither rule nor ruin {consequent denied loholty); 
.-. He is not a demagogue. 

He will either not rule or not ruin {consequent denied 
disjunctively)/ 
.-. Nothing — for if he does either, he may, or ma}' not, be 
a demagogue. 
He will either rule or ruin {consequent affirmed); 
.-. Nothing — for a madman or a fool might do that. 

He is not a demagogue {antecedent denied); 
.*. Nothing; — for the same reason. 






OUTLINES OF LOdK . 85 

Class 2. (Plurality of antecedents and single consequent) : 

If it has rained, or if a dew has fallen, the ground is wet. 
It has rained, or a dew has fallen [antecedent affirmed 

in tot 6) ; 
. •. The ground is wet. 

It has rained {antecedent affirmed partitivety) ; 

.•. The ground is wet. 

A dew has fallen {antecedent affirmed partitivety); 

.-. The ground is wet. 

The ground is not wet {consequent denied); 
.*. It has neither rained nor has a dew fallen. 

The ground is wet {consequent affirmed); 
.-. Nothing — it ma}' have been wetted by a street sprinkler. 

It has neither rained nor has the dew fallen {antecedent 
denied in toto); 
.*. Nothing — unless you are certain that the antecedent 
includes all possible conditions precedent to the con- 
sequent. 
It has not rained {antecedent denied in pari); 
.-. Nothing — the dew may have fallen. 

The dew has not fallen {antecedent denied in part); 
,\ Nothing — it may have rained. 

Class 3. (A plurality of antecedents and plurality of con- 
sequents) : 

If this man was aware of the nature of his deeds, he is a 
murderer ; if he was not aware, he is insane. 
But he either was or was not aw T are ; 
.*. He is either a murderer or insane. 






51 : d. Explain and illustrate Whately's idea of the 
dilemma. 

The "dilemma," according to Whately, is a syllogism 

w r hose major premiss is a hypothetico-disjunctive judgment, 
with a plurality of antecedents and a single consequent ; 
while its minor premiss is a disjunctive judgment, e. g. 

If A is B, or C is D, E is F ; 
But either A is B or C is D ; 
.-. In any case, E is F. 



86 OUTLINES OF LOGIC. 

If this man is either a murderer or insane, he ought to be 
shut up ; 

But he is either a murderer or insane ; 
.-. In any case, he ought to be " restrained of his personal 
liberty." 

The practical utility of this form of reasoning — which is 
governed by rules already stated and exemplified — is frequently 
illustrated in our courts of justice. 



52. Explain the nature of the Incomplete Syllogism, 
and give the classification under this head. 

The full and regular forms of the S} T llogism are much less 
frequently used than certain incomplete forms, which the reader, 
or hearer, is supposed to be capable of filling up for himself — 
the regular syllogism being employed as a standard to which 
all processes of reasoning may be reduced, and b}^ which they 
may be tested. Under the head of Incomplete Syllogisms, we 
recognize four principal forms : Enthymeme, Sorites, Prosy 1- 
logism and Episyllogism. 



52 : a. Define and illustrate Enthymeme, Sorites, 
Prosyllogism and Episyllogism. 

An " enthynieme " is a syllogism of which one premiss is un- 
expressed, or held 7 ev St>//(j3. e. g. " The freedmen are unfit 
to vote because they cannot read " — a full statement of which 
argument would be : 

Whoever cannot read, is unfit to vote ; 
The freedmen cannot read ; 
.-. They are unfit to vote. 

The suppressed premiss is generally — as in the case before 
us — the major premiss. 



OV PLINES OF i 



-7 



A heap) i> a chain-syllogism (Ger. 

abming several syllogisms, in the flrst flgore, 

in such a way that the predicate of one premiss becomes the 

ject of the next, until, in the conclusion, the predicate of 

the last premiss is affirmed of the subject of the first. The 

following diagram will illustrate these statements : 



A is in B, 
B is in C, 
C is in D, 
D is in E, 
A is in E. 




All the premisses save the first, are cc major." The sup- 
pressed conclusion of the first syllogism introduced in a 
^comes the suppressed minor premiss of the 
>nd syllogism ; and so on. Thus the " sorites" before us, 
analyzed into its component syllogisms, would be : 



A is in B, 
B is in C, 

[.-. A is in C] 

C is in D, 

A is in C] 
[.-. A is inD.] 

D is in E, 
[A is in D.] 
r. A is in E. 



88 



OUTLINES OF LOGIC. 




The prosyllogism, is a syllogism whose 
conclusion becomes a premiss in ano- 
ther syllogism which immediately fol- 
lows it. The episyllogism, is a syllo- 
gism which takes the conclusion of a 
syllogism that immediately precedes it 
for one of its premisses. The prosyllo- 
gism is, ordinarily, introduced to sup- 
port a doubtful premiss ; the episyllo- 
J/^ eisin, to carry a conclusion to a more 
pointed and satisfactoiy result. 

To illustrate both by one example : 
Whatever deserves any stud} T , deserves 
careful stud}' [major premiss of main 
syllogism] ; Logic deserves study 
[minor premiss of main s} T llogism] ; 
since it tends to discipline the mind 
[prosyllogism] ; Therefore, Logic de- 
serves careful study [conclusion of 
main S3 T llogism], and no true student 
will neglect it [episyllogism]. 

In this example, the prosyllogism and 
episyllogism appear as enthymemes — 
being indicated by the italicized words. 
The accompanying diagram (suggested 
by one of my pupils, Mr. C. C. Herrick) 
gives them expanded so as more clearly 
to illustrate their relation to the main 
syllogism. 



53. What two-fold division is recognized under the 
head of Applied Logic ? 

Applied Logic, — which considers the Laws of Thought in 






OUTLINES OF LOGIC. 89 

their application to the discovery of truth, — may be divided 
into two branches. The first, which is concerned with the 
exposure of incorrect processes of reasoning, treats of 
Fallacies. The second, which teaches how t'o make correct 
practical application of the Laws of Thought, is called 
Method. 

53 . a. Define a fallacy, a sophism, a paralogism. 

A " fallacy" is a form of reasoning which, though specious 
and delusive, is nevertheless radically defective. A fallacious 
argument which is used with the intention of deceiving others, 
is called a "sophism'' ; a fallacious argument by which he 
who uses it is himself deceived, is called a "paralogism. " The 
distinction is Moral, not Logical. The same argument may 
be to one man, a "sophism"; to another man, a "par- 
alogism." 

53: b. Define Method. 

The Port Royal Logic says: "Method may be called, in 
general, the art of disposing of a series of many thoughts, 
either for the discovery of truth, when w T e are ignorant of it ; 
or for proving it to others, when it is already known. Thus, 
there are two kinds of method— one for discovering truth, 
which may be called analysis, or the method of invention ; 
and the other for explaining it to others, which may be called 
synthesis, or the method of teaching." Cf. Jevons, Logic, 
p. 201 sq. 

54. Give a general Classification of Fallacies, and ex- 
plain the terms used in classification. 

Fallacies may be classified as : 

(1) Formal. 

(2) Semi-Material. 

(3) Material. 



90 OUTLINES OF LOGIC. 

Formal fallacies are those which exist in the " form" of the 
thought expressed, altogether apart from its " matter." They 
may be detected and exposed, by simply applying the rules 
which govern the conduct of the syllogism. For example : if 
a syllogism introduce more than three terms ; or draw an 
affirmative conclusion from premisses one of which is 
negative ; or any conclusion from premisses both of which are 
negative, it is palpably incorrect in form — whatever the 
matter of thought may be. 

A semi-material fallac} T , is a fallac3 T which really exists in 
the form of thought, but which can only be detected and ex- 
posed by reference to the matter, e. g. 

Light is contrary to darkness ; 
Feathers are light ; 
.*. Feathers are contrary to darkness. 

This humorous syllogism involves a fallacy in form, since it 
introduces four terms ; but the fact that it introduces four 
terms, is not apparent until we notice the different matter 
denoted by the word " light" in the two premisses. Under 
the head of u semi-material " fallacies, fall all cases of 
" ambiguous middle" — than which no fallac} T is more frequent 
or more deceptive. 

Material fallacies are correct in form, and give us a con- 
clusion which follows legitimately from the premisses 
assumed ; but they are defective in matter. 



54: a. Mention the ways in which a Material Fal- 
lacy may be involved in our reasoning. 

Material Fallacies may be involved in our reasoning : 

(1) By the unwarrantable assumption of a premiss. Thus: 
we may have a conclusion correctly drawn from a premiss 
which itself requires proof; or which, indeed, is utterly false. 

(2) By irrelevant conclusion, or, as it has been technically 






01 I LINES 01 LOOK . 91 

termed, ignoratio elenchi. Here, the premisses may be unim- 
peachable, and the conclusion may follow legitimately from 
them ; but it is not ad rem — it has no proper bearing on the 
question at issue. 

54: b. Enumerate some of the fallacies under the 
head of Irrelevant Conclusion. 

Under the head of Irrelevant Conclusion we recognize : 

(1) The argumentum ad verecundiam, or an appeal to respec^t 
for constituted authorities and existing institutions — as when 
woman's claim to vote is set aside, upon the consideration that 
she never has voted. 

(2) The argumentum ad ignorantiam, or assuming a point 
that ought to be proved, in case one's opponent or one's 
hearers cannot disprove it. 

(3) The argumentum ud populum, or an appeal to the pas- 
sions and prejudices of one's hearers — as when an advocate 
dwells on the danger of letting a criminal loose upon the com- 
munity, and draws a thrilling picture of the misery he has 
caused, instead of proving that he is a criminal. 

(4) The argumentum ad hominem, or a diversion of atten- 
tion from the question at issue to the personal unfitness of 
one's opponent to raise such a question, e. g. " You're a 
pretty fellow to accuse the Erie Road of rascality. How long- 
is it since you went down into the southern tier of counties to 
defend the corporation against just such a charge?" 

(5) Any argument, however respectable, that is not ad rem, 
or to the point. 

54 : c Enumerate and explain the fallacies under 
the head of Unwarrantable Assumption of 
a Premiss. 

Under the head of "unwarrantable assumption of a pre- 

we may include the following fallacies: 
(1) Petitio Principiii or begging the question — that is, 



92 OUTLINES OF LOGIC. 

virtually assuming in one premiss, the very thing that the 
argument is constructed to prove. "Thus," to borrow At- 
water's example, "if one undertakes to show that a given 
tariff will be beneficial, because it will promote the public 
wealth ; without proving this latter — he perpetrates a petitio 
principii" 

(2) Argumentum in circulo — in which the premisses are 
used to prove the conclusion ; and then the conclusion, to 

*prove the premisses. One of my students recently gave me 
the following capital illustration of this defect: " Wiry did 
the Saviour do this?" "To fulfill prophecy." "Why was 
the prophecy given?" " To be fulfilled." 

(3) Nbn causa pro causa, in which that which is merely an 
antecedent, is assumed as a cause : e. g. " Night invariably 
precedes day ; therefore, it is the cause of it." 

On the distinction between an antecedent and a cause, see 
Topic 10 : a. Cicero says: "Causa est ea quid efficit id 
cujus est causa. Xon sic causa intelligi debet, ut, quod cuique 
antecedat, id ei causa sit ; sed quod efficienter antecedat." 

The stock illustration of this fallacy (which is sometimes 
characterized as Post hoc; ergo, propter hoc) is embodied in 
the famous passage by Hugh Latimer concerning Tenterden 
Steeple and Goodwin Sands. [See Reed's Eng. Lit. p. 166.] 

(4) Non tale pro tali, in which we draw our conclusion from 
a similarity that is assumed, without sufficient proof, to 
exist, e.g. " All other religions are a delusion; therefore 
the Christian religion is a delusion." Here, there is a mani- 
fest assumption of the minor premiss, " The Christian religion 
is like all other religions" — which is the very point at issue. 

55. Enumerate and explain some of the more promi- 
nent fallacies which fall under the head of Ambiguous 
Middle. 

The most prominent fallacies under the head of Ambiguous 
Middle are : 



OUTLINES Or LOGIC. 93 

(1) The Fallacy of Composition and Division^ in which 
the middle term is taken individually in one premiss, and col- 
lectively in the other, e. g. 

3 and -1 are two numbers; (Division.) 

7 is 3 and 1 ; (Composition.) 
.*. 7 is two numbers. 

7 is one number ; (Composition.) 

3 and 4 is 7 ; (Division.) 
.*. 3 and 4 are one number. 

All the angles of a triangle are equal to two right angles ; 
A B C is an angle of a triangle ; 
.'. ABCis equal to two right angles. 

The Latin language has the advantage of ours here. It 
would use cunctl (co/<ju;icti), instead of omnes, in the major 
premiss, and thus utterly dodge the fallac} r . 

A kindred fallacy is especially common, where the word 
" all" is introduced in negative judgments ; since there ma}% 
obviously, be a question whether the negative modifies the 
copula or the adjective. To borrow an example from Whately : 
u If all testimony to miracles is to be admitted, the Popish 
legends are to be believed. But the Popish legends are not 
to be believed. Therefore, all testimony to miracles is not to 
be admitted." Here, the correct inference would be : Not 
all testimony to miracles is to be admitted. 

Satan is the first person known to have made use of this 
fallac}' ; for in the question: " Hath God said ye shall not 
eat of all the trees in the garden?" [Ileb.], he meant to in- 
sinuate that Eve was forbidden to eat of every tree, while she 
was forbidden to eat of only one. 

(2) The Fallaeia Accidentia^ which consists in using the 
middle term, in one premiss, in a general and commonly ac- 
cepted sense ; in the other, in a minute and special sense. 
e. (j. " Government [general] is a blessing; The most cruel 
despotism is a government [special] ; Therefore, the most 
cruel despotism is a blessing." 



94 OUTLINES OF LOGIC. 

(3) The Fallacy of Etymology, in which the middle term 
is used, in one premiss, in its strictly derivative ; in the other, 
in its commonly accepted, sense. We may take an example 
from Adam Smith's Wealth of Nations : "Projectors [i. e. 
men full of projects] ought not to be trusted ; This man is a 
projector [i. e. he has formed a project] ; Therefore, he ought 
not to be trusted." 

A similar fallacy consists in using a subject, or a predicate, 
in the premisses, in a different sense from that which it bears 
in the conclusion. Take, for instance, Home Tooke's argu- 
ment : 

"Truth [derivative sense, according to Tooke] is what 

one trows, or imagines" ; 
" What one trows, or imagines, is variable" ; 
.*. " Truth [in the commonly accepted sense] is variable. 

(4) The Fallacia Plurium Inter rog ant ium, which consists in 
adroitly blending with a question that one might, reasonably, 
be expected to answer promptly and unequivocally, another 
question, of a doubtful nature, which would be covered by the 
answer to the main question ; or a statement to which the 
answer to the main question would seem to give assent, e. g. 
"Why did the Saviour wish his disciples to have swords in 
the Garden of Gethsemane"? That is : Did he wish them to 
have swords; and, if so, why? "Did you introduce a reso- 
lution to fix a certain salary at a less rate than it has hereto- 
fore been?" Yes and no. I introduced a resolution to fix a 
certain salary ; but cutting it down was the result of an 
amendment over which I had no control. 

This fallacy is an especial favorite with the lawyers, and is 
the secret of many of their demands for " a categorical 
answer," when examining witnesses. Aristotle was shrewd 
enough to detect it, and emphasizes the wisdom of answering 
but one question at a time. 

(5) The Fallacia Fictae UniversaJitatis. which consists in a 






OUTLINES OF LOGIC. 



05 



groundless induct ion from a few cases to all cases, e. g. 
••some enterprises begun on Friday have turned out badly ; 
therefore, Friday is an unlucky day." " I never saw such an 
unhealthy place as Rochester." "Why?" "Because there 
has been a death in the Freshman class." 



56. Give a Tabular Analysis of Fallacies. 

r C Four Terms. 

! Negative Premisses. 
Formal: { Undistributed Middle. 
Worst Relation. 
Illicit Process. 

r Composition and Division. 
MatebiIl: J Fallacia Accidentis. ^ 

J Fallacia Etyraologiae i a * Y> 

(Ambiguous ) ( b. or P. 

Fallacia Plurium Interrogantium. 



FALLACIES. 



Middle.) 



Fallacia Fictae Universalitatis. 



Unwarrantable 
Assumption, i 



Material : { 



Petitio Princrpii. 
Arg. in Circulo. 
Non Causa pro Causa. 
I Non Tale pro Tali. 



Irrelevant 
Conclusion. 



f Arg. ad Verecundiam. 
I 



Ignorantiam. 
" Populum. 
" Hominem. 



57. Explain the difference, in object and method, be- 
tween Deductive and Inductive Reasoning. 

The mind, by process of induction, generalizes the indi- 
vidual phenomena which it notices, and arrives at general 
notions. By process of deduction, it unfolds the significance 
of these general notions, and applies the principles involved 



96 OUTLINES OF LOGIC. 

in them to particular cases. In other words: "Deduction 
consists in passing from more general to less general truths ; 
Induction is the contrary process — from less to more general. " 
Jevons, Princijjles of Science, vol. 1, p. 14. Thus, as the 
result of my observation of individual phenomena, I arrive, by 
induction, at the general notion that "all bodies, left free to 
fall, tend towards the earth." By deduction from this general 
notion, I arrive at the conclusion that "This pencil, if left free 
to fall, will tend towards the earth." Both the inductive and 
the deductive processes, fall within the scope of Logic ; but it 
is the deductive process which Logic has, until recently, 
especially emphasized. The tendency now is to attach equal 
— if not superior -importance to Inductive Logic; and this 
tendency is, doubtless, in the right direction. The old logi- 
cians were inclined to assume their premisses without ade- 
quate investigation, and rigidly deduce from them eveiy 
conclusion that they could possibty yield. Modern logicians 
scrutinize their premisses most carefully. Indeed, most 
recent logics— e. g. those of Mill, Bain and Fowler — devote 
more space to inductive than to deductive Logic. 

Hamilton (ed. of Reid's Works, p. 712, note) saj r s : " The 
Organon of Aristotle and the Organon of Bacon (t, e. deduction 
and induction) stand in relation ; but it is the relation of con- 
trariety. The one, considers the laws under which the subject 
thinks ; the other, the laws under which the object is known. 
To compare them together is to compare excellencies of differ- 
ent species. Each proposes a different end ; both, in different 
ways, are useful ; and both ought to be assiduously studied." 
On the nature, and degree, of our indebtedness to Bacon, with 
reference to induction, see Atlantic Monthly, p. 573 sq., 
vol. 22 ; Jevons, Logic, p. 255 ; Macaulay, Essays, vol. 2, 
p. 395. 

Jevons {Principles of Science, vol. 1, p. 139) claims that 
" It cannot be said that the inductive process is of greater 
importance than the deductive process ; because the latter 



OUTLINES OF LOGIC. i)7 

process is absolutely essential to the existence of the former. 
Each is the complement, and counterpart, of the other, * * 
so that the question of relative importance cannot arise." He 
regards Induction, however, as involving investigations of far 
higher difficulty, variety and complexity, than those of 
Deduction. 

57 : a. What are the questions of prime importance 
with reference to Inductive Reasoning ? 

(1) Have the phenomena from which we form our induction 
been carefully observed ? 

(2) Are they accurately stated ? 

(3) Has any obvious phenomenon been ignored, or dis- 
torted, in order to support a pre-conceived theory v 

(4) Are the observed phenomena sufficiently numerous and 
clear, to warrant the affirmation respecting a class, of what we 
observe in particular cases ? 

(5) Precisely what general inference do the particular 
phenomena under our consideration, substantiate? 

57 : b. Mention some of the criterions by which we 
may test the accuracy of our inductions. 

The first (and, theoretically, the most satisfactory) test, is 
that of simple enumeration — in which all the individual in- 
stances possible, are* scrutinized, and each is found to illustrate 
the principle that we affirm of the class. Practically, how- 
ever, this test is comparatively fruitless*, since we can never 
be certain that we have examined all the individual instances, 
and since we are seeking to go beyond our observation and 
experience, and make an affirmation concerning things that 
we have not seen as the result of examining things that we 
have seen. 

We endeavor, therefore, not only to identify, in as many 
cases as possible, the principle that we seek to affirm ; but 
to distinguish, in the cases which we observe, that causative 

9 



98 OUTLINES OF LOGIC. 

element which makes them what they are, and which mast pro- 
duce similar effects whenever it is suffered to work unchecked. 
Thus (to borrow an example from Atwater) we determine, by 
simple enumeration, that the orbits of all known planets are 
elliptical ; and, hence— on the general ground of the uni- 
formity of nature (belief in which, the disciples of Mill and 
Herbert Spencer enforce as an a priori truth) —are warranted 
in assuming that the orbits of all planets yet to be discovered, 
will prove to be elliptical. But this presumption is im- 
measurably enhanced, when we are able to affirm that the 
elliptical orbits of the planets, are the resultant of those 
centripetal and centrifugal forces that prevail throughout 
the universe. 



57 : c What principles should govern us in our 
search for causes? 

In searching for the causes that produce certain effects, 
we should remember : 

(1) That the assumed cause, or causes, must always be 
present where the effect is noticed. 

(2) That the effect must always follow where the assumed 
cause is noticed — unless we can detect the presence of some 
adequate counteracting agency. 

(3) That, as the assumed C3iise varies in intensit}', the effect 
must vary. For example : the theory that the mercury was 
sustained in the Torricellian tube b}- the pressure of the at- 
mosphere, was verified by taking the tube up a high mountain 
and ascertaining that the effect varied with its assumed cause. 

(I)- That we must be able to account for residual variations 
(or incidental phenomena), without invalidating the assumed 
cause. Under this head, Thomson (Laws of Thought, p. 254 
sq.) gives some fine illustrations — of which we reproduce one. 

" In Sir Humphrey Davy's experiments upon the decomposi- 
tion of water by galvanism, it was found that (besides the two 
components of water, oxj-gen and lrydrogen) an acid and an 



OUTLINES OF LOGIC. 90 

alkali were developed at the two opposite poles of the ma- 
chine. As the theory of the analysis of water did not give 
reason to expect these prodncts t they were a residual phenom- 
enon, the cause of which was still to be found. Some chem- 
ists thought that electricity luid the power of producing these 
substauces of itself; and if their erroneous conjecture had 
been adopted, succeeding researches would have gone upon a 
false scent, considering galvanic electricity as a producing 
rather than a decomposing force. The happier insight of Davy 
conjectured that there might be some hidden cause of this 
portion of the effect ; the glass vessel containing the water 
might suffer partial decomposition, or some foreign matter 
might be mingled with the water, and the acid and alkali be 
disengaged from it, so that the water w T ould have no share in 
their production. Assuming this, he proceeded to try whether 
the total removal of the cause, would destroy the effect ; or, at 
least, the diminution of it, cause a corresponding change in the 
amount of effect produced. By the substitution of gold ves- 
sels for the glass without any change in the effect, he at once 
determined that the glass was not the cause. Employing dis- 
tilled water, he found a marked diminution of the quantity of 
acid and alkali evolved ; still, there was enough to show that 
the cause, whatever it was, was still in operation. Impurity 
of the water, then, was not the sole, but a concurrent cause. 
He now conceived that the perspiration from the hands touch- 
ing the instruments might affect the case, as it would contain 
common salt, and an acid and an alkali would result from its 
decomposition under the agency of electricity. By carefully 
avoiding such contact, he reduced the quantity of the products 
still further, until no more than slight traces of them were 
perceptible. What remained of the effect, might be traceable 
to impurities of the atmosphere, decomposed by contact with 
the electrical apparatus. An experiment determined this : the 
machine was placed under an exhausted receiver, and when 
thus secured from atmospheric influence, it no longer evolved 
the acid and the alkali. 

Cf. Mill, Logic, B. 3, chapters 8 and 9. 

57 : d. Is it possible that an effect can have more 
than one cause ? 

When we seek to determine the cause of a given effect, 
there are three theories open to us : 



100 OUTLINES OF LOGIC. 

(1) That the effect has one invariable cause. 

(2) That the effect is due to one of two or more different 
causes — though different causes more frequently produce simi- 
lar effects than the same effects. [The student, by the waj-, 
who learns to discriminate between similar and same, has 
learned a very useful lesson.] 

(3) That the effect is due (which is frequently the case) to 
a combination of causes. 

In the first and third cases, the effect must always be accom- 
panied by the assumed cause. In the second case, the assumed 
cause may be now present, now absent ; but, when this is the 
case, we have, very possibly, confounded an accidental con- 
comitant with a cause. 

See Mill, Logic, Vol. 1, p. 482 sq. 

57 : e. Enumerate and explain the Methods of In- 
duction recognized by Mill. 

(1) The Method of Agreement, which consists in comparing 
different instances in which a given phenomenon occurs. The 
canon as stated by Mill {Logic, Vol. 2, p. 428) is : "If two 
or more instances of the phenomenon under investigation ha\ e 
only one circumstance in common, the circumstance in which 
alone all the instances agree, is the cause of the phenomenon." 
Thus (letting the capital letters represent antecedents, and 
the lower-case letters, consequents) if ABC give abc ; and 
ADE, ade ; A is, probably, the cause of a. BC cannot be, 
for the} T were not present in the last instance ; nor DE, for 
they were not present in the first. As the result of com- 
parison, we eliminate variable antecedents. "It is the one 
antecedent,' or group of antecedents, always present when the 
the effect is present, that we consider the cause." Jevons. 

(2) The Method of Difference, which consists in comparing 
instances in which the phenomenon occurs, with instances, in 
other respects similar, in which it does no.t occur. The canon, 
as stated by Mill, is : 



OUTLINES OF LOGIC. 101 

"If an instance in which the phenomenon under investiga- 
tion occurs and an instance in which it does not occur, have 
every circumstance in common save one — that one, occurring 
only in the former — the circumstance in which alone the two 
instances differ, is the cause, or an indispensable part of the 
cause, of the phenomenon. " 

Jevons's statement is full as clear and conclusive : " The 
antecedent which is invariably present when the phenomenon 
follows, and invariably absent when it is absent (other circum- 
stances remaining the same) is the cause of the phenomenon." 

Thus if ABC gives abc, and BC gives be ; A may be safely 
assumed as the cause of a. Our object, here, is to eliminate 
variable antecedents ; but by a different method. This second 
method is more decisive than the first ; but is better adapted 
to experiment than to observation. The chemist can bring- 
together ABC and BC, and note the difference in their respec- 
tive effects ; but the requisite combinations of antecedents 
may not present themselves in nature. Where the second 
method is feasible, the first naturally precedes it and prepares 
the way for it. 

(3) The Joint Method of Agreement and Difference, This 
method (which is useful where the second method is not avail- 
able) consists in a comparison of several cases in w r hich a 
occurs, with several cases in which it does not occur. Thus : 
ABC, ADE, AFG, all yield a; HIJ, KLM, NOP, do not. 
Here we establish a connection not only between the presence 
of A and the presence of a; but between the absence of A 
and the absence of a. Hence, we arrive, substantially, at the 
" Method of Difference": 

ABC yields abc, 

BC " be, 

.-.A " a. 

The canon of this method, as stated b} T Mill (Logic, vol. 1, 
p. 435) is: " If two or more instances in which the phenome- 
non occurs have only one circumstance in common, while two 



102 OUTLINES OF LOGIC. 

or more instances in which it does not occur have nothing in 
common save the absence of that circumstance ; the circum- 
stance in which alone the two sets of instances differ, is 
the cause, or an indispensable part of the cause, of the 
phenomenon." 

(4) The Method of Residues, which proceeds by subtracting 
from an}' given phenomenon all the portions that, by pre- 
vious inductions, can be assigned to known causes. Thus : 

If ABC yields abc, 
B " b, 
C " c, 



This is, in reality, but a modification of the " Method of 
Difference" ; but is frequently available where that is not. 

The canon of this method, as stated by Mill (Logic, vol. 1, 
p. 437) is: " Subduct from an}' phenomenon such part as is 
known, by previous inductions, to be the effect of certain 
antecedents ; and the residue of the phenomenon is the effect 
of the remaining antecedents." 

(5) The Method of Concomitant Variations. The canon of 

this method (which is useful in determiniDg the relations of 

"permanent causes, or indestructible natural agents") is : 

64 Whatever phenomenon varies in any manner whenever 

another phenomenon varies in a particular manner, is either a 

cause, or an effect, of that phenomenon ; or is connected with 

it by some fact of causation" — as, for instance, a common 

cause. Thus : 

If A yields a, 

A 2 " a 2 , 

A " a; 

2~ T 

there is some causal connection between A and a. One is the 
cause of the other, or the}' are both related to a common 
cause. 



OUTLINES OF LOGIC. 103 

58. What is the nature and value of the Argument 
from Analogy, and what especial caution is necessary 
in its use ? 

The Argument from Analogy is an inference of resemblance 
between objects and classes, in certain particulars where 
resemblance has not been observed, on the ground of an 
observed resemblance in certain other particulars. 

This argument falls, mainly, within the scope of Inductive 
Logic ; and is of slight value in establishing a point, since it 
merely creates a presumption in favor of our position. In 
refuting objections, it is far more useful, and has been largely 
employed in religious controversy — notably, by Bishop Butler. 
e. g. It is inferred from the suffering of even the innocent in 
this life, that the suffering of the guilty in the life to come, is 
not incompatible with the nature of God. This argument is, 
however, mainly useful as a guide in our search for those 
underlying causes, or general principles, which may serve as a 
substantial basis of classification. In emplo3'ing it, we should 
be especially careful that the resemblances which we note are 
actual, essential, and as numerous as possible ; and that the 
resemblances which we predicate, fall within the same category 
as those which we note. Otherwise, we become involved in 
the fallacy Non tale pro tali. Cf. Mill, Logic, p. 491 sq., 
Amer. ed. 

e. g. If A and B. are known to be admirers of Teniryscn, 
and A. is, also, known to be a lover of Wordsworth ; we may 
safely predict that B, also, will be a lover of Wordsworth — 
since Wordsworth and Tennyson are, in many respects, 
similar. But we cannot, on the ground of A.'s liking o} T sters, 
predict that B will like oysters ; since the similarity of tastes 
previously established between A and B is intellectual —not 
gustatoiy. 

2. What is the nature, and what are the uses and tests, 
of Scientific Hypothesis ? 

Scientific hypotheses are explanations of observed pheno- 



104 OUTLINES OF LOGIC. 

mena, which are provisionally accepted to account for those 
phenomena until, b} r observation and reflection, we can deter- 
mine the real principle upon which those phenomena depend. 
These hypotheses are originated by those thoroughly trained 
minds which seem to be naturally endowed with a keen per- 
ception of analogies ; and are instrumental in promoting that 
search for causes which transmutes scientific conjectures into 
scientific principles. See Thomson, §115. Thej^ are useful, 
also (like the rod and wires that give form to the skeleton) 
in enabling us to grasp, and retain, those apparently related 
facts which are likely to be dissociated, or altogether lost, 
unless we do group them about a common centre. 

The only danger that results from our employment of 
hypotheses, arises from our liability to forget that the hypo- 
thesis which we have accepted, is only an enlightened con- 
jecture, requiring to be verified — not, a fact. 



60. What Distinction is to be made between hypo- 
theses, theories, systems ? 

A sharp distinction is to be made between the words 
"hypothesis" and " theory" ; though they are often used 
interchangeably. By "hypothesis," we are to understand 
the conjectural explanation of certain phenomena by reference 
to an assumed cause ; by " theory," the conjectural explana- 
tion of certain phenomena by reference to a real cause. The 
cause must, in the latter case, be known to produce effects 
similar to those which we seek to explain ; and the value of 
the theory will correspond to the nature and degree of that 
similarity. By proving the existence of the cause assumed in 
an hypothesis, the hypothesis is verified, and becomes a 
" theory." By proving that the cause thus shown to exist, is 
actually the cause of the phenomena under consideration, the 
theory is verified, and becomes a fact, or if at all compli- 
cated—a svstem. 



01 TLINE3 OF LOGIC. 105 

A proposed hypothesis should be rigidly subjected to the 
following tests : 

(1) It must not be assumed to account for what can be ex- 
plained on known principles. 

(2) It must be adequate to account for all the known facts 
in a given case. 

(3) It must be independent of subsidiary hypotheses. To 
illustrate : Biot, to account for the Northern Lights, pro- 
pounded the hypothesis that they are caused by the play of 
electricity through immense columns of minute particles of 
iron, suspended in the region of the pole — a Irypothesis which 
is defective in that it leaves unsolved the questions : Where 
do the particles of iron come from ? ; and how are they held in 
position ? 

See Fleming, Vocab. of Phil — snb voce " Hypothesis.". 

61. What classifications have been proposed, within 
the sphere which Applied Logic embraces ? 

The sphere of Applied Logic embraces all that about which 
the mind thinks ; and may be roughly classified as including : 

(1) The ego. 

(2) The non-ego. 

(3) That absolute being which is neither the ego nor the 
non-ego. See Thomson, p. 246. 

Not content, however, with this general classification, phil- 
osophers have sought to give minute and exhaustive divisions 
of the province of thought. 

See Atwater, pp. 213-216, for the categories of Aristotle, 
Kant, M'Cosh/Mill and Thomson. 

Though this subject falls rather within the scope of Meta- 
physics than that of Logic, I append a rearrangement of the 
Aristotelian " categories" — i. e. the classes into which our 
thoughts must fall — which is suggested by Hamilton in his 
Logic, p. 139 sq. and subsequently worked out in his edition 
of Reid, p. 687 note. This table — which Hamilton does not 



10G 



OUTLINES OF LOGIC. 



regard as exhaustive, but as being correct so far as it goes — 
may serve, at least, to show that Aristotle, in his world-re- 
nowned categories, co-ordinates disparate species. It is to be 
noticed that the Stoics had already reduced Aristotle's catego- 
ries to four: Substance, Quality, Quantity and Relation. 

CLASSIFICATION OF CATEGORIES. 

Ens. 
TO ON 



Ens per se. 
ovcria 



r~ 



Ens per accidens. 

A 



Absolute. 



Matter. 
rtoGov 2 



Form. 

noiov 2. 



Relative. 



n: 



Posture. 



Habit. 

» 8 



Place. Time. Action, 
7rov b 7t6re 6 or 

Passion. 
7toieir d 

7ta(jx eiyl ° 

The Greek words in the above table, indicate the categories 
as designated b} r Aristotle ; the numbers, the order in which 
he arranged them. Hamilton quotes from Murmelius the fol- 
lowing mnemonic lines which may serve to recall the Aristo- 
telian categories : 

Arbor 1 sex 2 servos 4 fervore 3 refrigerat 9 ustos 10 ; 
Run 5 eras 6 stabo r , nee tunicatus 8 ero. 
Cf. Bain, Mental Science, Amer. ed., p. 17 note and The 
Scriblerus Papers, Ch. 7, Pope's Works, Vol. 6, p. 152. 



62. Indicate the relation of Applied Logic to Scien- 
tific Discovery ? 

While Logic is susceptible of practical application to all the 
matters about which we think — however diversified and dis- 
connected ; it aims, especially, to accomplish : 

(1) The Construction of Sciences, by referring particular 
phenomena, in any department of inquiry, to a general princi- 



OUTLINES OF LOGIC. 107 

pie ; identifying that principle with a cause ; and defining and 
classifying all its effects. 

It is only by the rigid and persistent application oi the 
Laws of Thought that any science can be constructed ; and, 
thus, even physical science is dependent, for its very being, 
on the laws of that immaterial existence which it* so often 
slights and depreciates. Alexander Bain sa} T s (Deductive 
Logic, p. 2G) : "There can be no science without assuming 
all the data of Logic, whether avowedly or not." The same 
point is abundantly conceded by Jevons in his admirable 
Principles of Science. Logic is not, therefore, as many have 
thought, a thing of the dead past. It belongs to the living 
present. Independent of it, no science — whether mental or 
physical — is possible. 

(2) Logic contemplates the Classification of the Sciences, so 
as to exhibit their mutual relation, and their common depen- 
dence on the Great First Cause. The statement and criticism 
of the results attained by Logic in this direction, belong, 
rather, to Metaphysics. See, however, Thomson, pp. 315— 
320 ; Atwater, p. 109 ; and Bain, Deductive Logic, pp. 23-30. 

Bain — whose Classification of the Sciences is the best I have 
yet seen — gives as 

Departmental Sciences. 

1. Logic. 

2. Mathematics. 

3. Mechanical Physics. 

4. Molecular Physics. 
6. Chemistry. 

6. Biology. 

7. Psychology. 

An eighth should, I think, be added — namely : 

8. Theology. 



EXAMPLES FOR LOGICAL PRAXIS. 



I. Point out the defects in the following arguments: 

1. All that glitters is not gold. This watch glitters. Therefore, it 
is not gold. 

2. Oaks are vegetable. Oysters are not oaks. Therefore, oysters 
are not vegetable. 

3. What we eat grows in the fields or is the flesh of animals. Cooked 
food is what we eat. Therefore, cooked food grows in the field or is the 
flesh of animals. 

4. Typhoid fever is epidemic, because A, B, and C, have it. 

5. He who calls you a man, speaks truly. He who calls you a fool, 
calls you a man. Therefore, he who calls you a fool, speaks truly. 

6. No pagan is a Christian. Every villager is a pagan. Therefore, 
no villager is a Christian. 

7. If a man is a kind father, he will provide food and clothing for 
his children. Mr. A. provides food and clothing for his children. 
Therefore, he is a kind father. 

8. Animal food may be entirely dispensed with, and vegetable food 
may be entirely dispensed with. But all food is either animal food or 
vegetable food. Therefore, all food may be entirely dispensed with. 

9. Nothing is heavier than platinum. Feathers are heavier than 
nothing. Therefore, feathers are heavier than platinum. 

' 10. These people are patriots because they are free. 

11. He who is most hungry, eats most. He who eats least, is most 
hungry. Therefore, he who eats least, eats most. 

12. Whatever is universally believed, must be true. The existence of 
God is not universally believed. Therefore, it is not true. 

13. A successful author must either be very industrious or very 
talented. Gibbon was very industrious. Therefore, he was not very 
talented. 

14. God is in every place. This room is not every place. Therefore, 
God is not in this room. 

15. An inflated currency promotes national prosperity, because it 
enables people to make rapid fortunes. 

10 



110 OUTLINES OF LOGIC. 

16. " Improbable events happen almost every day ; but what happens 
almost every day is a very probable event. Therefore, improbable 
events are very probable events." — Whately. 

17. Hard substances are elastic; for ivory is both hard and elastic. 

18. We have satisfactory evidence that Mr. A. did not take a bribe 
during the last session of the assembly. Therefore, he is entirely 
worthy of the suffrages of the people. 

19. Mahomet was a wise law-giver; for he studied the character of 
his people. 

20. M He would not take the crown. Therefore, 'tis certain he is not 
ambitious." 

21. " Last evening Rev. J. T. Kendrick lectured at Neptune Hall, 
No. 405 Grand street, on Temperance. He argued that if alcohol had 
been necessary for man, God would have provided it for him at the 
creation ; and that, as alcohol is produced by the decay of vegetable 
matter, it cannot give health or strength, or sustain the life of animals." 

22. "Aussi ne peut on echapper a ce dilemme: S'il y a quelque 
benefice a retirer d'une industrie, ella n'a pas besoin d' encouragement: 
S'il n'y a point de benefice a en retirer, elle ne merite pas d* etre 
encouragee." — Blanqui, Economie Politique, p. 75. 

23. Books are a source both of instruction and amusement. A table 
of logarithms is a book. Therefore, a table of logarithms is a source 
both of instruction and amusement. 

24. "If it is fated that you shall recover from the present disease, 
then you will recover, whether you call in a physician or not. If it is 
fated that you shall not recover, then, with or without a physician, you 
will not recover. But either the one or the other of these is fated. 
Therefore, it will be of no use to call in a physician." — Cicero. 

25. It is universally conceded that careful and assiduous vocal train- 
ing is absolutely essential to good singing ; therefore, careful and assidu- 
ous vocal training is absolutely essential to good speaking. 



II. Explain the nature of the following arguments, and com- 
plete THOSE THAT ABE IMPERFECT. ARE ANY OF THEM FALLACIOUS? 

If so, in what respect? 

26. Plants are bodies with organization. Potatoes are plants. 
Therefore — 

27. Ireland is idle, and therefore starves ; she starves, and therefore 
rebels. 

28. The child of Themistocles governed his mother; she governed 
her husband ; her husband governed Athens ; Athens, Greece ; and 
Greece, the world. Therefore, the child of Themistocles governed the 
world. 



OUTLINES OF LOGIC. Ill 

29. Any one who is candid will refrain from condemning a book 
without reading it. Some reviewers do not refrain from this. There- 
fore, some reviewers are not candid. 

30. Every effect must have an adequate cause. Therefore, the world 
must have been created. 

31. Cogito; ergo, sum. — Des Cartes. 

32. The cars stop at Waterloo one half the time. The cars carry the 
mail one half the time. Therefore — 

33. The cars stop at Waterloo one-half the time. The cars carry the 
mail three-fourths of the time. Therefore — 

34. "The prisoner was at the place at the time of the murder. He 
participated in the motives which led to the commission of the murder. 
He owned, and usually carried with him, the weapon with which the 
murder was committed. He shared in the means afterwards taken to 
divert attention from those who were actually engaged in committing 
the murder. Therefore, the prisoner is guilty." — Webster in the Knapp 
case. 

35. The dog, the fox, the wolf and the jackal, are carnivorous. The 
dog, the fox, the wolf and the jackal are all animals having canine teeth. 
Therefore, all animals having canine teeth are carnivorous. 

36. Now a mediator does not appertain to one, but God is one. — 

Gal 3: 20. 

37. The Devil to Cuvier : " I have come to eat you." Cuvier to the 
Devil : "Cloven hoofs — Horns — Come on !" 

38. "There is none good but one, that is God. Christ is good, 
therefore he is God; or Christ is not God, therefore he is not good." — 
Stier. 

39 "Shall that be shut to man which to the beast is open?" — Par. 
Lost, B. 9 : 691-692. 

40. "Of good, how just? of evil, if what be evil be real, why not 
known, since easier shunned ?" — Par. Lost, B. 9 : 698-699. 

41. " Only a good man can be an orator, for intelligence would not 
be conceded to those who choose the worse rather than the better course, 
nor prudence to those who subject themselves to punishment." — Quin- 
tilian. 

42. "For as many are of the works of the law are under the curse; 
for it is written, Cursed is every one that continueth not in all things 
which are written in the book of the law to do them. But that no man 
is justified by the law in the sight of God it is evident : for the just shall 
live by faith. And the law is not of faith ; but, the man that doeth 
them shall live in them." — Gal. 3 : 10-11. 

43. Newsboy: "Here's the Evening Express, only two cents." 
Passenger : " I'll take one " Newsboy (after supplying his customer) : 
"Here's the Evening Express, only three cents." 



112 OUTLINES OF LOGIC. 

44. The Christian religion is not recognized by the law of the land, 
because it is not even mentioned by the Constitution of the United 
States 

45. The Hebrews were forbidden to make to themselves the likeness 
of anything that is in the heaven above, or in the earth beneath, or in 
the waters under the earth. Therefore, the cherubim are not real 
existences. 

4(5. Gold and silver are wealth ; and therefore the diminution of the 
gold and silver in the country by exportation, is a diminution of the 
wealth of the country. 

47. " All men have their price." 

48. "The barrenness of the soil in Northeastern Siberia, and the 
severity of the long winter, led man to domesticate the reindeer as the 
only means of obtaining a subsistence ; the domestication of the rein- 
deer necessitated a wandering life ; a wandering life made sickness and 
infirmity unusually burdensome to both sufferers and supporters ; and 
this finally led to the murder of the old and sick, as a measure both of 
policy and niercy." — Tent Life in Siberia, p. 215. 

49. Force and matter are inseparable. Therefore, there can have 
been no creation of matter. — Biichner. 

50. " Our professor is opposed to sectarian colleges; therefore, he 
favors irreligious colleges." 

III. Miscellaneous examples to be reduced to strict logical 

FORM ; TESTED ; AND, W T HERE NECESSARY AND POSSIBLE, REFUTED. 

51. It is the duty of a government which takes charge of the educa- 
tion of its citizens, to provide for them such an education as they can 
conscientiously avail themselves of. The only education that Roman 
Catholics can conscientiously avail themselves of, is one conducted by 
priests, who shall inculcate the tenets of their church pari passu with 
secular knowledge. Therefore, it is the duty of our government to pro- 
vide such an education. 

52. [In reply to 51.] " Other folks have consciences as well as the 
Roman Catholics." — A Student. 

53. It is the duty of a state to provide for its citizens such educa- 
tional facilities as will qualify them, in the highest degree, for the dis- 
charge of their social and political duties. The only education which 
can thus qualify them, must have its foundation in religious principles. 
Therefore, the Bible should be retained in the common schools. 

54. On the same principle which is urged as an objection to retaining 
the Bible in the common schools, the Roman Catholic might object to 
making use of any text books which contain extracts from the Bible, or 
are founded on the truths of the Bible. But to abandon these text 
books, would be to forego the enlightenment and civilization of the 
nineteenth century. Therefore, the Bible should not be removed from 
the schools. 



OUTLINES OF LOGIC. 113 

55. To make a man pay for instruction of which he cannot conscien- 
tiously avail himself, is contrary to the spirit of our institutions. 

The retention of the Bible in schools supported by indiscriminate 
taxation, makes Roman Catholics pay for instruction of which they can- 
not conscientiously avail themselves. Therefore, either the Roman 
Catholic should be excused from paying for the support of the common 
school system, or the Bible, against which he objects, should be removed 
from the schools. 

But to excuse the Roman Catholic from paying for the support of the 
common school system, would be a greater evil than the banishment of 
the Bible from the common schools ; for the retention of the Bible is of 
but slight practical value, while to excuse the Roman Catholic from con- 
tributing for the support of our schools, would lead to the education of 
many children under influences hostile to the republic. Therefore, the 
Bible should be banished from the schools. 

56. [In reply to 55.] " The Romanists manifest no especial regard 
for 'the spirit of our institutions.' " — A Student. 

57. [In reply to 55.] "If we yield this point to gratify the con- 
sciences of one body of men, we must keep on yielding to gratify other 
bodies of men, till we have no school system left." — A Student. 

58. [In reply to 55.] "If the Irish Catholics don't like the institu- 
tions of the country which has afforded them protection, let them go 
back whence they came." — A Student. 

59. To remove the Bible from the common schools would tend to 
hasten the downfall of Romanism, by inducing greater religious activity 
among Protestants. 

60. "If the Bible be read in our schools, it must be either with com- 
ments or without. But to read it without comments suffers that to pass 
as the Word of God which is the interpolation, or mistranslation, of 
man ; while to read it with comments, would be to open the door to sec- 
tarian instruction. Therefore, the Bible should not be retained in the 
schools." — A Student. 

61. "The laws of the land do not, and cannot, take cognizance of 
any religious sect. But if the Bible be removed from the schools, it 
would be on account of the claims of a sect. Therefore, the Bible 
should not be removed from the schools." — A Student. 

62. Any true education is impossible save in connection with religious 
instruction. But the state has no right to interfere with the religious 
instruction of its children. Therefore, the state has no right to main- 
tain a system of common schools. — Bp. McQuaid. 

63. [In refutation of 62.] "If the words 'religious instruction' 
have reference to 'the recognition of God as an object of worship, love 
and obedience,' the minor premiss is unwarrantably assumed ; if the 
words ' religious instruction ' refer to the inculcation of the tenets of 
any particular system of faith and worship, the major premiss is unwar- 
rantably assumed. But the words ' religious instruction ' must be used, 
throughout the syllogism, in one of these senses, else the syllogism in- 
volves four terms. Hence the Bishop's argument is fallacious." — A 
Student. 



114 OUTLINES OF LOGIC. 

64. u Perhaps the most noticeable thing in this part of the reverend 
Doctor's discourse is the holy horror of crosses and saints which he dis- 
plays. ' The Catholic child,' he says, k comes with his crosses and saints 
upon his back,' while the Presbyterian or Baptist leaves his peculiarities 
behind him. Truly, a convenient religion, which can be taken along or 
left at home at pleasure!" — A Catholic Citizen. 

65. Imagine a Democrat going to the school board and saying : " My 
boy must not read the Constitution of the United States, except in an 
exclusively Democratic school, where it will be expounded to him eccord- 
ing to the tenets of the Democratic faith." — N. H. Statesman. 

66. We ought not to insist on the retention of the Protestant Bible 
in our schools, unless we are willing to acquiesce in the admission of the 
Douay version if the Romanists should come to be in the majority. 

67. True prayer, implies belief that God will hear and answer. Pray- 
ing to see whether God will hear and answer, implies a doubt in these 
respects, and is, therefore, not true prayer. To pray, and, at the same 
time, not to pray, is the negation of thought. 

68. True prayer implies acquiescence in the will of God. To demand 
of God specific answers, foregoes such acquiescence. Therefore, Tyn- 
dall's proposed prayer test is impossible. 

69. " Tyndall's proposed prayer test seems to me ridiculous, for 
twenty years ago, God converted my soul." 

70. " God's answers to prayer are the gifts of a father to his children. 
To pray as Professor Tyndall proposes, would be to show an unfilial 
spirit, which would justify an earthly parent in witholding his accus- 
tomed gifts from a child. " — A Student. 

71. Science recognizes both observation and experiment as legitimate 
means of verifying physical phenomena. Why, then, should it be pro- 
posed to restrict the testing of prayer to experiment ? 

72. If, as some claim, Tyndall's proposed prayer test has already been 
applied, and that with divine sanction, in the case of Elijah and the 
prophets of Baal, what objection to applying it now ? 

73. Mr. Pendleton having said, in one of his sophomoric speeches, 
that it was an appalling fact that there wasn't money enough in the 
country, by $150,000,000, to pay the taxes of the nation and states, if 
the people were required to pay them all in one day, Senator Morton 
replies as follows in his Cincinnati speech : ' ' Well, now, that is a tre- 
mendous thought ; and it is also an appalling fact that if the people 
were required- to eat, in one day, all they now eat in the course of a 
year, they would inevitably burst." 

74. The more correct the logic, the more certainly the conclusion 
will be wrong if the premisses be false. Therefore, where the premisses 
are wholly uncertain, the best logician is the least safe guide. 

7."). Logic, as it was cultivated by the Schoolmen, proved a fruitless 
study. Therefore, Logic as it is cultivated at the present day, must 
prove a fruitless study. 



INDEX. 



{The references are to pages.'] 

Accident, defined 43 

Added determinants, immediate inference from 64 

Ambiguous middle, fallacy of 90, 92 

Analogy, argument from 103 

Analysis and synthesis 16, 71, 89 

Antecedent, discriminated from cause 19, 82, 92 

A priori truths 16, 98 

Argumentum in circulo 92 

Argumentum ad populum, etc 81 

Aristotelian categories, rearrangement of 106 

Aristotelian dictum concerning predicate 45 

Bacon, our indebtedness to 93 

Barbara, celarent, darii, ferioque, etc.. 79 

Bimembral division, importance of 36 

Categorical judgments 44 

Categories, classification of 106 

Cause and effect, nature of "..19, 82, 92 

Causes, how guided in our search for 98, 103 

Causes, possible multiplicity of 99 

Cognitive faculties, defined 6 

Composition and division, fallacy of 93 

Composition of judgments, immediate inference from 64 

Conative faculties, defined 6 

Concept, defined — method of forming 21 

Conception, defined 16, 20 

Conception, judgment and reasoning related 1" 

Conceptualists, opinions of 26 

Conditional judgments 44 

Conditional syllogism 81 

Connotative terms 31 

Contradictory and contrary opposition 57 

Conversion , defined 61 

Conversion, simplified by Hamilton 62 

Coordinate species, defined 30 

Copula, different interpretations of 49 

10 



116 INDEX. 

Definition, Logical defined 37, 43 

Demonstration, distinguished from proof 54 

Denomination, importance of 23 

Deduction, discriminated from induction 95 

Denotative terms 31 

Dictum, de omni et nullo 77 

Differentia, defined 28 

Differentia, a concurrent genus 39 

Dilemma 44. 85 

Discursive faculties, discriminated 6 

Disjunctive judgments, immediate inference from 65 

Disjunctive syllogism 83 

Disparate species, defined 30 

Distribution, Logical explained 45 

Division, Logical , 35 

Division, importance of bimembral 36 

Elocution, its relation to Rhetoric 4 

Emotive faculties, defined 6 

Empiricists, opinions of 15 

Enthymeme 86 

Episyllogism 88 

Essence, defined 28 

Excluded middle, principle of 18 

Extension, Logical discussed 30 

Faculties, mental defined and classified 4: 

Fallacia accidentis 93 

Fallacia fictas universalitatis 94 

Fallacia plurium interrogantium 94 

Fallacies, formal, material, semi-material 89 

Fallacies, table of 95 

Fallacy, defined 89 

Fallacy of etymology 94 

Figure Logical, explained 75 

Figure Logical, its present insignificance 77, 81 

Form, distinguished from matter 10 

Genus, defined 28, 43 

Genus, summum 30 

Hamiltonian additions to Aristotelian judgments 47 

Hamiltonian judgments, value of 49, 53 

Hamiltonian significance of the copula 49 

Hamiltonian simplification of conversion 62 

Hamiltonian use of " some," 52, 59 

Hamilton on Extension and Intension 32, 49 

Hamilton on Logical Figure 77, 81 

Hypothesis, nature of scientific 104 

Hypothetical syllogism 81 

Hy pothetico-dis junctive syllogism 84 



INDEX. 117 

Idealists, opinions of 14 

Identity, principle of 18 

Ignoratio elencbi !»1 

Illicit process 7 

Imagination, its Logical significance 5 

Imagination, its nature and functions 8 

Immediate inference, defined and classified...., 

Immediate inference, importance of <;«; 

Imperfect disjunction, dangers of 66 

Inconsistent opposition 58 

Individual .defined 28 

Inductive reasoning, analysis of 97 

Induction, discriminated from deduction 95 

Induction, Mill's methods of 100 

Inference, mediate and immediate 56 

Infima species, not absolutely fixed 33 

Intension, defined and discriminated 30 

Intension, validity of reasoning in G9 

Interpretation, immediate inference of 66 

Intuition, defined 20 

Intuitive faculties, discriminated 6 

Irrelevant conclusion 90 

Judgment, defined 16, 40 

Judgment, different methods of reading 31, 67 

Judgments, categorical and conditional ■ 44 

Judgments, Hamiltonian discussed 48, 53 

Judgments, substitutive and attributive 42, 43 

Judgments, table of 47 

Judgments, universal and particular 41 

Language, its relation to thought 23 

Law. defined 9 

Logic, applied, classification under 89, 105 

Logic, a science 9 

Logic, benefits of studying , 12 

Logic, defined 9 

Logic, divisions of 16 

Logic, its relation to Psychology and Rhetoric 3 

Logic, its relation to scientific discovery 106 

Logic, pure and applied 12 

Logic, source of its materials 13 

Logic, true object of 11 

Logic, viewed analytically and synthetically 17 

Major premiss, defined 70 

Major term, defined and discussed 68 

Marks, defined and classified 28 

Matter, distinguished from form 10 

Memory, its nature and functions 7 

Method Logical, defined 89 

Methods of induction, Mill's 100 

Middle term, defined 68 



118 INDEX. 

Middle term, distribution of 73 

Mind, constitution of 15 

Mill J. S., methods of induction 100 

Minor premiss denned 70 

Minor term, denned and discussed . 68 

Mnemonic lines 79 

Modality, denned and discussed 54 

Modality, belongs to applied Logic 55 

Mood, Logical 78 

Moral and demonstrative reasoning 54 

Necessary laws of thought 11 

Necessary truths 16 

Nominalists, opinions of 25 

Non causa pro causa 92 

Non-contradiction, principle of 18 

Non tale pro tali 92, 103 

Notative and symbolic terms 24 

Object and objective, defined 6 

Opposition, denned and classified 56 

Opposition, tables of 59, 61 

Paralogism, defined 89 

Petitio principii, defined 91 

Positive concepts 34 

Predicate Aristotelian dictum concerning 45 

Predicable-cl asses, discussed 43 

Predicate, exists in the subject -, ,.. 32 

Predicate term, defined 68 

Premisses defined 70 

Premiss, unwarrantable assumption of , 90, 91 

Presentative faculties, discriminated 7 

Presentations, obscure and clear, confused and distinct, adequate 

and inadequate 29 

Privative concepts, their nature 34 

Privative concepts, immediate inference by 63 

Proof, discriminated from demonstration 55 

Property Logical, defined 43 

Proposition, defined 40 

Prosy llogism 88 

Proximate genus and species, defined 30 

Psychology, its relation to Logic 3 

Quality Logical, defined 41 

Quantity Logical, defined 40 

Realists, opinions of 14, 25 

Reason and consequent, nature of 19 

Reasoning, defined 16, 56 

Relation Logical, defined 42 

Relation Worst, discussed 73 



INDEX. 119 

Re-presentative faculties, discriminated 7 

Rhetoric, its relation to Logic 3 

Rhetorical definition 38 

Senses, credibility of 14 

Sciences, classification of 107 

"Some," Hamiltonian use of word 52, 59 

Sophism, defined , 89 

Sorites 87 

Species, defined 28 

Species infima 30 

Structural functions of human mind 15 

Subaltern genera and species 30 

Subaltern opposition 58 

Sub-contrary opposition 59 

Subject and subjective, defined 6 

Subject, exists in the predicate 32 

Subject-term, defined 71 

Sufficient reason, principle of 19 

Suggestive faculties, their training 13 

Summation of predicates, immediate inference by 65 

Summum genus, not absolutely fixed 33 

Sumption and sub-sumption, defined 70 

Supersensuous truths, defined 16 

Syllogism, defined and analyzed 67 

Syllogism, incomplete defined and classified 86 

Syllogism, rules for the conduct of 68 

Syllogisms, conditional, hypothetical, etc.... 81 

Syllogism, the unfigured 77 

Terms, denotative and connotative 31 

Terms, notative and symbolic 24 

Terms of a judgment, defined 40 

Terms of a syllogism, defined 68 

Theory, discriminated from hypothesis 104 

Thought, defined 8 

Thought, fundamental laws of 17 

Thought, its relation to language 23 

Transcendentalists. opinions of 15 

Undistributed middle 74 

Worst Relation 73 

Y, reducible to U 53 



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